What is the relation between the two vectors A = 2 i + 5 j - 6 k and B = i + (5)/(2) j - 3 k ?

Correct answer: B. A is parallel to B Given vectors are A = 2 i + 5 j - 6 k and B = i + (5)/(2) j - 3 k . Taking 2 common from the components of A : A = 2( i + (5)/(2) j - 3 k ) A = 2 B Since A is a scalar multiple of B , the two vectors are parallel. Answer: A is parallel to B

MHT CET 202624 AprilEvening Shift

Exam: MHT CET
Year: 2026
Date: 24 April
Shift: Evening Shift
Subject: Physics
Chapter: Mathematics in Physics

MHT CET 2026 · 24 April · Evening Shift · Physics · Mathematics in Physics

What is the relation between the two vectors A = 2 i + 5 j - 6 k...

What is the relation between the two vectors

\vec{A} = 2\hat{i} + 5\hat{j} - 6\hat{k}

and

\vec{B} = \hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k}

Options

A $\vec{A}$ is perpendicular to $\vec{B}$
B $\vec{A}$ is parallel to $\vec{B}$
C $\vec{A} + \vec{B} = 0$
D $\vec{A} - \vec{B} = 0$

Correct answer

B. $\vec{A}$ is parallel to $\vec{B}$

Step-by-step solution

Given vectors are

\vec{A} = 2\hat{i} + 5\hat{j} - 6\hat{k}

and

\vec{B} = \hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k}

.

Taking

2

common from the components of

\vec{A}

\vec{A} = 2(\hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k})

\vec{A} = 2\vec{B}

Since

\vec{A}

is a scalar multiple of

\vec{B}

, the two vectors are parallel.

Answer:

\vec{A}

is parallel to

\vec{B}

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