First slide

Vectors

Question

$\vec{A} = \sqrt{2} \hat{i} + \sqrt{2} \hat{j} and \vec{B} = \overset{\land}{i} + \overset{\land}{j}$ then the vector parallel to $\vec{A}$ and having the magnitude $\vec{B}$ is

Moderate

A

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

$\sqrt{2} \overset{\land}{i} + \sqrt{2} \overset{\land}{j}$
C

$2 \hat{i} + 2 \hat{j}$
D

$\frac{1}{\sqrt{2}} \overset{\land}{i} + \frac{1}{\sqrt{2}} \overset{\land}{j}$

Solution

$\hat{A} = \frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j} a n d B = \sqrt{1^{2} + 1^{2}} = \sqrt{2} T h e n, \vec{C} = B \hat{A} = \hat{i} + \hat{j}$

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