First slide

Vectors

Question

If $a \hat{i} + b \hat{j}$ is a unit vector and it is perpendicular to $\hat{i} + \hat{j}$ , then value of a and b is

Moderate

A

1, 0
B

$-$ 2, 0
C

0.5, $-$ 0.5
D

None of these

Solution

$(a \hat{i} + \hat{b_{j}}) \cdot (\hat{i} + \hat{j}) = 0 or a + b = 0$ …(i)
Further, $\sqrt{a^{2} + b^{2}} = 1 or a^{2} + b^{2} = 1$ …(ii)
Solving Eqs. (i) and (ii), we get
$a = \pm \frac{1}{\sqrt{2}} and b = \pm \frac{1}{\sqrt{2}}$

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