First slide

Scalars and 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 $α, β and γ$ with x, y and z axis respectively then $α = β = γ$
$\begin{array}{l} \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \\ \Rightarrow 3 \cos^{2} α = 1 \Rightarrow \cos α = \frac{1}{\sqrt{3}} \\ ∴ A_{x} = A_{y} = A_{z} = A \cos α = \frac{A}{\sqrt{3}} \end{array}$

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