Suppose two vectors are given by a = 4 i + 3 j and b = 3 i + 4 j . Compute the magnitude of a + b .

Correct answer: B. 7 2 Given vectors are a = 4 i + 3 j and b = 3 i + 4 j . The sum of the vectors is given by: a + b = (4 i + 3 j ) + (3 i + 4 j ) a + b = 7 i + 7 j The magnitude of the resultant vector is: | a + b | = 7^2 + 7^2 | a + b | = 49 + 49 = 98 = 7 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

Suppose two vectors are given by a = 4 i + 3 j and b = 3 i + 4 j ....

Suppose two vectors are given by

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

and

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

. Compute the magnitude of

\vec{a} + \vec{b}

Options

A $14$
B $7\sqrt{2}$
C $10$
D $7$

Correct answer

B. $7\sqrt{2}$

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 sum of the vectors is given by:

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

\vec{a} + \vec{b} = 7\hat{i} + 7\hat{j}

The magnitude of the resultant vector is:

|\vec{a} + \vec{b}| = \sqrt{7^2 + 7^2}

|\vec{a} + \vec{b}| = \sqrt{49 + 49} = \sqrt{98} = 7\sqrt{2}

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