First slide

Vectors

Question

The component of vector $A = 2 \hat{i} + 3 \hat{j}$ along the vector $\hat{i} + \hat{j}$ is

Moderate

A

$\frac{5}{\sqrt{2}}$
B

$10 \sqrt{2}$
C

$5 \sqrt{2}$
D

5

Solution

$\frac{\vec{A} . \vec{B}}{| \hat{i} + \hat{j} |} = \frac{(2 \hat{i} + 3 \hat{j}) (\hat{i} + \hat{j})}{\sqrt{2}} = \frac{2 + 3}{\sqrt{2}} = \frac{5}{\sqrt{2}}$

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