Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-component of r?
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Solution
The x-component of r is 2.
Correct Answer:
A
— 2
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Q. If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)
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Solution
The x-coordinate of point P is the coefficient of i in the position vector, which is 2.
Correct Answer:
A
— 2
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Q. If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?
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Solution
Distance = |r| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Correct Answer:
A
— 5
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Q. If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?
A.
They are equal
B.
They are parallel
C.
They are orthogonal
D.
They are collinear
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Solution
If A · B = 0, then A and B are orthogonal (perpendicular) to each other.
Correct Answer:
C
— They are orthogonal
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Q. If the scalar product of two vectors A and B is 15 and the magnitudes are |A| = 5 and |B| = 3, find the angle between them.
A.
60°
B.
45°
C.
30°
D.
90°
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Solution
A · B = |A||B|cos(θ) => 15 = 5*3*cos(θ) => cos(θ) = 1, θ = 0°.
Correct Answer:
B
— 45°
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Q. If the scalar product of two vectors A and B is equal to the product of their magnitudes, what can be inferred?
A.
They are perpendicular
B.
They are parallel
C.
They are equal
D.
They are opposite
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Solution
If A · B = |A||B|, then the angle between them is 0°, meaning they are parallel.
Correct Answer:
B
— They are parallel
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Q. If the scalar product of vectors A and B is equal to the product of their magnitudes, what can be said about the angle between them?
A.
0°
B.
90°
C.
180°
D.
45°
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Solution
If A · B = |A||B|, then cos(θ) = 1, which means θ = 0°.
Correct Answer:
A
— 0°
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Q. If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?
A.
-3i - 4j - 5k
B.
3i + 4j + 5k
C.
0
D.
None of the above
Show solution
Solution
The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.
Correct Answer:
A
— -3i - 4j - 5k
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Q. If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
A.
10i + 24j
B.
5i + 12j
C.
2i + 3j
D.
7i + 14j
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Solution
Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.
Correct Answer:
A
— 10i + 24j
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Q. If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)
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Solution
A · B = (1)(2) + (2)(1) = 2 + 2 = 4
Correct Answer:
B
— 5
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Q. If the vectors A = 2i + 2j and B = 2i - 2j, find A · B.
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Solution
A · B = (2)(2) + (2)(-2) = 4 - 4 = 0.
Correct Answer:
B
— 4
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Q. If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?
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Solution
Since A and B are perpendicular, A · B = 0.
Correct Answer:
A
— 0
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Q. If the vectors A = 3i + 4j and B = 4i + 3j, what is the scalar product A · B?
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Solution
A · B = (3)(4) + (4)(3) = 12 + 12 = 24.
Correct Answer:
A
— 25
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Q. If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?
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Solution
A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.
Correct Answer:
B
— 0
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Q. If the vectors A = 6i + 8j and B = 2i + 3j, what is A · B? (2020)
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Solution
A · B = (6)(2) + (8)(3) = 12 + 24 = 36.
Correct Answer:
A
— 42
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Q. If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)
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Solution
A · B = (6)(3) + (8)(4) = 18 + 32 = 50, but since they are perpendicular, A · B = 0.
Correct Answer:
A
— 0
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Q. If the vectors A and B are such that A · B = |A| |B|, what is the angle between them?
A.
0°
B.
90°
C.
180°
D.
None of the above
Show solution
Solution
If A · B = |A| |B|, then cos(θ) = 1, which means θ = 0°.
Correct Answer:
A
— 0°
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Q. If vector A = 2i + 3j + k and vector B = i - 2j + 4k, what is the cross product A × B?
A.
-10i + 5j + 7k
B.
10i - 5j - 7k
C.
10i + 5j + 7k
D.
-10i - 5j + 7k
Show solution
Solution
A × B = |i j k|\n|2 3 1|\n|1 -2 4| = (3*4 - 1*(-2))i - (2*4 - 1*1)j + (2*(-2) - 3*1)k = 10i - 5j - 7k.
Correct Answer:
A
— -10i + 5j + 7k
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Q. If vector A = 2i + 3j and vector B = -i + 4j, what is the resultant vector R = A + B?
A.
i + 7j
B.
i + j
C.
3i + 7j
D.
3i + 4j
Show solution
Solution
R = A + B = (2 - 1)i + (3 + 4)j = 1i + 7j.
Correct Answer:
A
— i + 7j
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Q. If vector A = 2i + 3j and vector B = 3i + 4j, what is the angle between them? (2023)
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.6, θ = 53.13 degrees.
Correct Answer:
D
— 60 degrees
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Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between A and B? (2023)
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (8 + 15) / (√(13) * √(41)). θ = 60 degrees.
Correct Answer:
D
— 60 degrees
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Q. If vector A = 2i + 3j and vector B = 4i + 5j, what is the angle between them?
A.
0 degrees
B.
90 degrees
C.
45 degrees
D.
60 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (2*4 + 3*5) / (√(2^2 + 3^2) * √(4^2 + 5^2)) = 0.5, θ = 60 degrees.
Correct Answer:
D
— 60 degrees
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Q. If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if scaled
Show solution
Solution
Vectors A and B are parallel because B = 2A.
Correct Answer:
A
— Yes
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Q. If vector A = 2i + 3j and vector B = 4i + k, what is the angle between A and B?
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A| |B|). A · B = 8 + 0 + 3(0) = 8; |A| = √(2^2 + 3^2) = √13; |B| = √(4^2 + 1^2) = √17. θ = cos^(-1)(8/(√13 * √17)).
Correct Answer:
B
— 60 degrees
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Q. If vector A = 3i + 4j and vector B = 2i - j, what is the dot product A · B?
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Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer:
A
— 10
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Q. If vector A = 3i + 4j and vector B = 4i + 3j, what is the cross product A × B?
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Solution
A × B = |i j k| |3 4 0| |4 3 0| = (0 - 0)i - (0 - 0)j + (9 - 12)k = -3k.
Correct Answer:
B
— 1k
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Q. If vector A = 4i + 3j and vector B = -3i + 4j, what is the angle between them?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (4*-3 + 3*4) / (5*5) = 0, θ = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)
A.
3i + 5j
B.
5i + j
C.
3i + j
D.
5i + 5j
Show solution
Solution
A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.
Correct Answer:
A
— 3i + 5j
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Q. If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector R = A + B? (2019)
A.
3i + 5j
B.
5i + j
C.
3i + j
D.
5i + 5j
Show solution
Solution
R = A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.
Correct Answer:
A
— 3i + 5j
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Q. If vector A = 4i + 3j and vector B = 3i + 4j, what is the angle between A and B?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
135 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (12 + 12) / (5 * 5) = 24/25, θ = cos^(-1)(24/25) ≈ 60 degrees.
Correct Answer:
B
— 60 degrees
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Showing 91 to 120 of 156 (6 Pages)
Vector Algebra MCQ & Objective Questions
Vector Algebra is a crucial topic in mathematics that plays a significant role in various school and competitive exams. Mastering this subject not only enhances your understanding of mathematical concepts but also boosts your confidence in solving objective questions. Practicing MCQs and important questions in Vector Algebra can greatly improve your exam preparation and help you score better.
What You Will Practise Here
Understanding vector addition and subtraction
Scalar and vector products
Applications of vectors in geometry
Key formulas related to vector magnitudes and directions
Representation of vectors in different coordinate systems
Concept of unit vectors and their significance
Solving problems involving vector equations
Exam Relevance
Vector Algebra is frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that involve calculations, conceptual understanding, and application of vector principles. Common question patterns include solving for resultant vectors, determining angles between vectors, and applying vector operations in real-world scenarios.
Common Mistakes Students Make
Confusing scalar and vector quantities
Misapplying vector addition and subtraction rules
Neglecting the importance of direction in vector problems
Overlooking the significance of unit vectors
Failing to visualize vectors geometrically
FAQs
Question: What are some important Vector Algebra MCQ questions I should focus on?Answer: Focus on questions related to vector addition, scalar and vector products, and applications in geometry.
Question: How can I improve my understanding of Vector Algebra for exams?Answer: Regular practice of objective questions and solving previous years' exam papers can significantly enhance your understanding.
Start solving practice MCQs today to test your understanding of Vector Algebra and prepare effectively for your exams. The more you practice, the more confident you will become in tackling this essential topic!
