First slide

Vectors

Question

Vector $\vec{A}$ makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of $\vec{A}$ ) will be

Moderate

A

$\frac{A}{\sqrt{3}}$
B

$\frac{A}{\sqrt{2}}$
C

$\sqrt{3} A$
D

$\frac{\sqrt{3}}{A}$

Solution

Let the components of $\vec{A}$ makes angles $α, β a n d γ w i t h x, y a n d z a x i s r e s p e c t i v e l y t h e n α = β = γ$
$\cos^{2} θ + \cos^{2} β + \cos^{2} γ = 1$
$\Rightarrow 3 \cos^{2} θ = 1 \Rightarrow cosα = \frac{1}{\sqrt{3}}$
$∴ A_{x} = A_{y} = A_{z} = Acosα = \frac{A}{\sqrt{3}}$

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