First slide

Vectors

Question

If $\vec{A} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ then the direction cosines of the vector $\vec{A}$ are

Moderate

A

$\frac{2}{\sqrt{5}}, \frac{4}{\sqrt{45}} and \frac{- 5}{\sqrt{45}}$
B

$\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}} and \frac{3}{\sqrt{45}}$
C

$\frac{4}{\sqrt{45}}, 0 and \frac{4}{\sqrt{45}}$
D

$\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}} and \frac{5}{\sqrt{45}}$

Solution

$\vec{A} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}$ $∴ | \vec{A |} = \sqrt{{(2)}^{2} + {(4)}^{2} + {(- 5)}^{2}} = \sqrt{45}$
$∴ cosα = \frac{2}{\sqrt{45}}, cosβ = \frac{4}{\sqrt{45}}, cosγ = \frac{- 5}{\sqrt{45}}$

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