First slide

Vectors

Question

The angle between $A = \hat{i} + \hat{j} and B = \hat{i} - \hat{j}$ is [NCERT Exemplar]

Easy

A

$45^{0}$
B

$90^{0}$
C

$- 45^{0}$
D

18 $0^{0}$

Solution

Given, $A = \hat{i} + \hat{j} and B = \hat{i} - \hat{j}$
We know that, $A \cdot B = | A ‖ B | \cos θ$
$\Rightarrow (\hat{i} + \hat{j}) \cdot (\hat{i} - \hat{j}) = (\sqrt{1 + 1}) (\sqrt{1 + 1}) \cos θ$
where, $θ$ is the angle between A and B.
$\Rightarrow \cos θ = \frac{1 - 0 + 0 - 1}{\sqrt{2} \sqrt{2}} = \frac{0}{2} = 0 \Rightarrow θ = 90 °$

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