First slide

Vectors

Question

If three vectors along coordinate axes represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be

Moderate

A

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

$\frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{36}}$
C

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

$\frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}$

Solution

Diagonal vector, $A = b \hat{i} + b \hat{j} + b \hat{k}$
or $A = \sqrt{b^{2} + b^{2} + b^{2}} = \sqrt{3} b$
$∴ \hat{A} = \frac{A}{| A |} = \frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}$

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