Vector vecA makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of vecA ) will be

Question

Vector vecA makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of vecA ) will be (A) (A/√3) (B) (A/√2) (C) √3 A (D) (√3/A)

Tardigrade Admin · Accepted Answer

Let the components of vecA makes angles α, β and &gamma; with x, y and z axis respectively then α=β=&gamma; cos 2 α+ cos 2 β+ cos 2 &gamma;=1 ⇒ 3 cos 2 α=1 ⇒ cos α=(1/√3) ∴ Ax=Ay=Az=A cos α=(A/√3)

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

$\frac{A}{3}$

$\frac{A}{2}$

$3 A$

$\frac{3}{A}$

Let the components of $A$ makes angles $α, β$ and $γ$ with $x, y$ and $z$ axis respectively then $α = β = γ$
$cos^{2} α + cos^{2} β + cos^{2} γ = 1$
$\Rightarrow 3 cos^{2} α = 1$
$\Rightarrow cos α = \frac{1}{3}$
$∴ A_{x} = A_{y} = A_{z} = A cos α = \frac{A}{3}$

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

3​A​

2​A​

3​A

A3​​