1. Tardigrade
  2. Question
  3. Physics
  4. Vector vecA makes equal angles with x, y and z axis. Value of its components (in terms of magnitude of vecA ) will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Motion in a Plane

Solution:

Let the components of $\vec{A}$ makes angles $\alpha, \beta$ and $\gamma$ with $x, y$ and $z$ axis respectively then $\alpha=\beta=\gamma$
$ \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 $
$\Rightarrow 3 \cos ^{2} \alpha=1 $
$\Rightarrow \cos \alpha=\frac{1}{\sqrt{3}}$
$\therefore A_{x}=A_{y}=A_{z}=A \cos \alpha=\frac{A}{\sqrt{3}}$