First slide

Scalars and Vectors

Question

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

Moderate

A

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

$10 \sqrt{2}$
C

$5 \sqrt{2}$
D

$5$

Solution

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

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