First slide

Vectors

Question

The angle between the vectors $(\hat{i} + \hat{j}) and (\hat{j} + \hat{k})$ is

Moderate

A

$30^{0}$
B

$45^{0}$
C

$60^{0}$
D

$90^{0}$

Solution

$((\hat{i} + \hat{j}) . (\hat{j} + \hat{k}) = 0 + 0 + 1 + 0 = 1)$
$cosθ = \frac{\vec{A} . \vec{B}}{| \vec{A} | | \vec{B} |} = \frac{1}{\sqrt{2} \times \sqrt{2}} = \frac{1}{2} ∴ θ = 60^{0}$

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