Question

A vector is equally inclined to all of the coordinates axes then the angle made by it with X-axis is theta then -
(A) cos theta = 2/√3
(B) cos theta = 1/√3
(C) sin theta = 2/√3
(D) sin theta = 1/√3

Note: It is a Multiple correct question answers are more than one

Plzz help me out​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{A vector is equally inclined to the co-ordinate axes}$

$\underline{\textbf{To find:}}$

$\textsf{The angle made by the vector with the x-axis}$

$\underline{\textbf{Solution:}}$

$\textsf{Let}$ $\boldsymbol{\alpha,\beta\;\&\;\gamma}$ $\textsf{be the angles made by the}$

$\textsf{given vector with co-ordinate axes}$

$\textsf{As per given data,}$

$\boldsymbol{\alpha=\beta=\gamma}$

$\textsf{But,}\;\textbf{Sum of the squares of direction cosines is 1}$

$\implies \boldsymbol{cos^2\alpha+cos^2\beta+cos^2\gamma=1}$

$\implies\; \boldsymbol{cos^2\alpha+cos^2\alpha+cos^2\alpha=1}$

$\implies \boldsymbol{3\,cos^2\alpha=1}$

$\implies \boldsymbol{cos^2\alpha=\dfrac{1}{3}}$

$\implies \boldsymbol{cos\alpha=\dfrac{1}{\sqrt{3}}}$

$\underline{\textbf{Answer:}}$

$\textsf{Option (B) is correct}$