Q. If vector A = 4i + 3j and vector B = 4i - 3j, what is the angle between A and B? (2019)
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = 16 - 9 = 7. |A| = 5, |B| = 5. cos(θ) = 7/(5*5) = 0.28, θ = 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the angle between them?
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = (5)(-5) + (12)(12) = -25 + 144 = 119. Since A and B are in opposite directions, the angle is 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = -5i + 12j, what is the resultant vector A + B? (2021)
A.
0i + 24j
B.
10i + 0j
C.
0i + 12j
D.
5i + 12j
Show solution
Solution
A + B = (5 - 5)i + (12 + 12)j = 0i + 24j.
Correct Answer:
A
— 0i + 24j
Learn More →
Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the angle between A and B?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (5*12 + 12*(-5)) / (√(169) * √(169)) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 5i + 12j and vector B = 12i - 5j, what is the value of A × B?
Show solution
Solution
A × B = |i j k| |5 12 0| |12 -5 0| = (0 - 0)i - (0 - 0)j + (5*-5 - 12*12)k = -85k.
Correct Answer:
A
— -85
Learn More →
Q. If vector A = 5i + 12j and vector B = 5i - 12j, what is the angle between A and B?
A.
0 degrees
B.
90 degrees
C.
180 degrees
D.
45 degrees
Show solution
Solution
A · B = 5*5 + 12*(-12) = 25 - 144 = -119. Since A · B < 0, angle is 180 degrees.
Correct Answer:
C
— 180 degrees
Learn More →
Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between A and B?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (√(50) * √(50)) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 5i + 5j and vector B = 5i - 5j, what is the angle between them?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
135 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (25 - 25) / (5√2 * 5√2) = 0, θ = 90 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. If vector A = 6i + 8j, what is the unit vector in the direction of A? (2023)
A.
3/5 i + 4/5 j
B.
6/10 i + 8/10 j
C.
1/5 i + 2/5 j
D.
2/5 i + 3/5 j
Show solution
Solution
Magnitude |A| = √(6^2 + 8^2) = 10. Unit vector = (1/10)(6i + 8j) = (3/5)i + (4/5)j.
Correct Answer:
A
— 3/5 i + 4/5 j
Learn More →
Q. If vector G = 4i - 3j + 2k, what is the y-component of G?
Show solution
Solution
The y-component of G is -3.
Correct Answer:
B
— -3
Learn More →
Q. If vector J = 5i + 12j, what is the angle between J and the positive x-axis?
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
tan(θ) = 12/5; θ = tan^(-1)(12/5) which is approximately 67.38 degrees, closest to 60 degrees.
Correct Answer:
C
— 60 degrees
Learn More →
Q. If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?
A.
i + 5j
B.
i + j
C.
3i + 5j
D.
3i + j
Show solution
Solution
K + L = (2i + 2j) + (-i + 3j) = (2 - 1)i + (2 + 3)j = 1i + 5j = i + 5j.
Correct Answer:
A
— i + 5j
Learn More →
Q. If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?
Show solution
Solution
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
Correct Answer:
C
— 10
Learn More →
Q. If vectors A and B are perpendicular, then A · B equals:
Show solution
Solution
If A and B are perpendicular, then by definition A · B = |A||B|cos(90°) = 0.
Correct Answer:
A
— 0
Learn More →
Q. The angle between the vectors A = i + j and B = j + k is:
A.
45°
B.
60°
C.
90°
D.
30°
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (0) / (√2 * √2) = 0, thus θ = 90°.
Correct Answer:
C
— 90°
Learn More →
Q. The magnitude of the vector A = 4i - 3j + 12k is:
Show solution
Solution
Magnitude |A| = √(4^2 + (-3)^2 + 12^2) = √(16 + 9 + 144) = √169 = 13.
Correct Answer:
B
— 14
Learn More →
Q. The scalar product of two unit vectors is 0. What can be inferred about these vectors?
A.
They are parallel
B.
They are orthogonal
C.
They are collinear
D.
They are equal
Show solution
Solution
If the scalar product is 0, the vectors are orthogonal.
Correct Answer:
B
— They are orthogonal
Learn More →
Q. The scalar product of two unit vectors is 0.5. What is the angle between them?
A.
60°
B.
30°
C.
90°
D.
120°
Show solution
Solution
cos(θ) = 0.5, θ = cos⁻¹(0.5) = 60°.
Correct Answer:
A
— 60°
Learn More →
Q. The scalar product of two vectors A and B is 12, and the angle between them is 60°. If |A| = 4, find |B|.
Show solution
Solution
A · B = |A||B|cos(θ) => 12 = 4|B|(0.5) => |B| = 6.
Correct Answer:
B
— 8
Learn More →
Q. The unit vector in the direction of vector A = 6i - 8j is:
A.
3/5 i - 4/5 j
B.
6/10 i - 8/10 j
C.
1/5 i - 4/5 j
D.
2/5 i - 3/5 j
Show solution
Solution
Unit vector = A/|A| = (6i - 8j)/√(6^2 + (-8)^2) = (6i - 8j)/10 = 3/5 i - 4/5 j.
Correct Answer:
A
— 3/5 i - 4/5 j
Learn More →
Q. What is the angle between the vectors A = 2i + 2j and B = 2i - 2j?
A.
0 degrees
B.
45 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (8) / (√8 * √8) = 1, θ = 0 degrees.
Correct Answer:
C
— 90 degrees
Learn More →
Q. What is the angle between the vectors A = i + j and B = 2i + 2j?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
30 degrees
Show solution
Solution
cos(θ) = (A · B) / (|A||B|) = (1*2 + 1*2) / (√2 * √8) = 4 / (2√2) = √2. θ = 45 degrees.
Correct Answer:
A
— 45 degrees
Learn More →
Q. What is the cross product of vectors A = i + 2j + 3k and B = 4i + 5j + 6k?
A.
-3i + 6j - 3k
B.
-3i + 6j + 3k
C.
3i - 6j + 3k
D.
3i + 6j - 3k
Show solution
Solution
A × B = |i j k| |1 2 3| |4 5 6| = -3i + 6j - 3k.
Correct Answer:
A
— -3i + 6j - 3k
Learn More →
Q. What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)
Show solution
Solution
A × B = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.
Correct Answer:
A
— -2k
Learn More →
Q. What is the cross product of vectors E = i + 2j and F = 3i + 4j?
Show solution
Solution
E × F = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (1*4 - 2*3)k = -2k.
Correct Answer:
A
— -2k
Learn More →
Q. What is the magnitude of the vector C = 5i - 12j?
Show solution
Solution
Magnitude |C| = √(5^2 + (-12)^2) = √(25 + 144) = √169 = 13.
Correct Answer:
A
— 13
Learn More →
Q. What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?
Show solution
Solution
Projection = (A · B / |B|^2) * B = (11 / 5) * (1i + 2j) = 2.5.
Correct Answer:
A
— 2.5
Learn More →
Q. What is the projection of vector A = 3i + 4j onto vector B = 2i + 0j?
Show solution
Solution
Projection of A onto B = (A · B / |B|^2)B. A · B = 6, |B|^2 = 4. Projection = (6/4)(2i) = 3i.
Correct Answer:
A
— 6
Learn More →
Q. What is the projection of vector A = 3i + 4j onto vector B = 2i + 2j?
Show solution
Solution
Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.
Correct Answer:
A
— 5
Learn More →
Q. What is the projection of vector A = 6i + 8j onto vector B = 2i + 2j?
Show solution
Solution
Projection of A onto B = (A · B / |B|^2) * B = ((6*2 + 8*2) / (2^2 + 2^2)) * (2i + 2j) = (28/8)(2i + 2j) = 7i + 7j.
Correct Answer:
A
— 8
Learn More →
Showing 121 to 150 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!
