First slide

Scalars and Vectors

Question

The vector component of $3 \hat{i} + 4 \hat{j} along \hat{i} + \hat{j}$ is

Moderate

A

$\frac{\hat{i} + \hat{j}}{2}$
B

$\frac{3}{2} (\hat{i} + \hat{j})$
C

$\frac{5}{2} (\hat{i} + \hat{j})$
D

$\frac{7}{2} (\hat{i} + \hat{j})$

Solution

Component of $\vec{A}$ along $\vec{B}$ is
$\frac{\vec{A} . \vec{B}}{B} = \frac{3 + 4}{\sqrt{2}} = \frac{7}{\sqrt{2}}$
In vector form, component of $\vec{A}$ along $\vec{B}$ is
$\frac{7}{\sqrt{2}} \hat{B} = \frac{7}{\sqrt{2}} \frac{\vec{B}}{B} = \frac{7}{\sqrt{2}} (\frac{\hat{i} + \hat{j}}{\sqrt{2}}) = \frac{7}{2} (\hat{i} + \hat{j})$

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