Given the vectors a = 4 i + 3 j and b = 3 i + 4 j , evaluate the magnitude of a .

Correct answer: A. 5 Given vector a = 4 i + 3 j The magnitude of the vector is given by | a | = x^2 + y^2 Substituting the components x = 4 and y = 3 : | a | = 4^2 + 3^2 | a | = 16 + 9 | a | = 25 = 5

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

Given the vectors a = 4 i + 3 j and b = 3 i + 4 j , evaluate the...

Given the vectors

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

and

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

, evaluate the magnitude of

\vec{a}

Options

A $5$
B $1$
C $7$
D $25$

Correct answer

A. $5$

Step-by-step solution

Given vector

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

The magnitude of the vector is given by

|\vec{a}| = \sqrt{x^2 + y^2}

Substituting the components

x = 4

and

y = 3

|\vec{a}| = \sqrt{4^2 + 3^2}

|\vec{a}| = \sqrt{16 + 9}

|\vec{a}| = \sqrt{25} = 5

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