Vector Algebra for Competitive Exam Success

Alerts Wishlist Cart

Vector Algebra

Q. Find the magnitude of the vector A = 3i - 4j. (2020)

A. 5
B. 7
C. 10
D. 12

Solution

|A| = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Learn More →

Q. If A = 2i + 3j and B = 3i + 4j, what is the angle between A and B? (2021)

A. 0 degrees
B. 45 degrees
C. 90 degrees
D. 180 degrees

Solution

cos(θ) = (A · B) / (|A||B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.7071, θ = 45 degrees.

Correct Answer: B — 45 degrees

Learn More →

Q. If A = 3i + 4j and B = 2i - j, what is A + B? (2021)

A. 5i + 3j
B. 5i + 5j
C. 1i + 5j
D. 1i + 3j

Solution

A + B = (3i + 4j) + (2i - j) = (3 + 2)i + (4 - 1)j = 5i + 3j.

Correct Answer: A — 5i + 3j

Learn More →

Q. If A = 4i + 2j and B = -i + 3j, what is the scalar triple product A · (B × A)? (2023)

A. 0
B. 8
C. 12
D. 16

Solution

B × A = |i  j  k| |-1  3  0| |4  2  0| = 0, hence A · (B × A) = 0.

Correct Answer: A — 0

Learn More →

Q. If A = 5i + 12j, what is the unit vector in the direction of A? (2021)

A. (5/13)i + (12/13)j
B. (12/13)i + (5/13)j
C. (5/12)i + (12/5)j
D. (12/5)i + (5/12)j

Solution

Unit vector = A / |A| = (5i + 12j) / √(5^2 + 12^2) = (5/13)i + (12/13)j.

Correct Answer: A — (5/13)i + (12/13)j

Learn More →

Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is A - B? (2023)

A. -3i - 3j - 3k
B. -3i - 3j + 3k
C. 3i + 3j + 3k
D. 3i + 3j - 3k

Solution

A - B = (1 - 4)i + (2 - 5)j + (3 - 6)k = -3i - 3j - 3k.

Correct Answer: A — -3i - 3j - 3k

Learn More →

Q. What is the cross product of vectors A = i + j and B = j + k? (2022)

A. i + k
B. i - k
C. j - i
D. k - j

Solution

A × B = |i  j  k| |1  1  0| |0  1  1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.

Correct Answer: A — i + k

Learn More →

Q. What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

A. 5
B. 10
C. 11
D. 14

Solution

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

Correct Answer: B — 10

Learn More →

Q. What is the projection of vector A = 3i + 4j onto vector B = i + j? (2020)

A. 3
B. 4
C. 5
D. 7

Solution

proj_B(A) = (A · B / |B|^2)B = ((3*1 + 4*1) / (1^2 + 1^2))(i + j) = (7/2)(i + j) = 3.5.

Correct Answer: C — 5

Learn More →

Showing 1 to 9 of 9 (1 Pages)

Biology (School & UG)

Chemistry (School & UG)

Civil Engineering

Commerce & Accountancy

Computer Science & IT

Current Affairs & GK

Data Structures & Algorithms

eBooks

Electrical & Electronics Engineering

English (School)

General Aptitude

General Knowledge

General Knowledge & Current Affairs

Languages & Literature

Law & Legal Studies

Major Competitive Exams

Mathematics (School)

Mechanical Engineering

Medical Science

Physics (School & Undergraduate)

Quantitative Aptitude & Reasoning

Social Science (School)

Technical

Verbal and Reasoning

Vocational & Skill Development

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely