Two vectors are defined as a = 4 i + 3 j and b = 3 i + 4 j . Determine the magnitude of a - b .

Correct answer: A. 2 Given vectors are a = 4 i + 3 j and b = 3 i + 4 j . The difference between the two vectors is given by: a - b = (4 i + 3 j ) - (3 i + 4 j ) a - b = (4 - 3) i + (3 - 4) j = i - j The magnitude of the resultant vector is: | a - b | = (1)^2 + (-1)^2 | a - b | = 1 + 1 = 2

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

Two vectors are defined as a = 4 i + 3 j and b = 3 i + 4 j ....

Two vectors are defined as

\vec{a} = 4\hat{i} + 3\hat{j}

and

\vec{b} = 3\hat{i} + 4\hat{j}

. Determine the magnitude of

\vec{a} - \vec{b}

Options

A $\sqrt{2}$
B $0$
C $2$
D $1$

Correct answer

A. $\sqrt{2}$

Step-by-step solution

Given vectors are

\vec{a} = 4\hat{i} + 3\hat{j}

and

\vec{b} = 3\hat{i} + 4\hat{j}

.

The difference between the two vectors is given by:

\vec{a} - \vec{b} = (4\hat{i} + 3\hat{j}) - (3\hat{i} + 4\hat{j})

\vec{a} - \vec{b} = (4 - 3)\hat{i} + (3 - 4)\hat{j} = \hat{i} - \hat{j}

The magnitude of the resultant vector is:

|\vec{a} - \vec{b}| = \sqrt{(1)^2 + (-1)^2}

|\vec{a} - \vec{b}| = \sqrt{1 + 1} = \sqrt{2}

Practice Physics and Mathematics on Quantrex Academy →

More from Physics and Mathematics