Question

If $θ1,θ2, θ3$ are the angles made by a line with the positive directions of the $x,y,z$ axes, then the value of $cos^{2}θ_1 +cos^{2}θ_2+cos^{2}θ_3$ is

• A. $-1$
• B. $1$
• C. $2$
• D. $-2$
• E. $0$

Answer 1

Answer: (B)

$1$

Answer 2

Given that

The line makes angles with the$x, y,z$ axes, the direction cosines of the line are given by $cos(θ_1), cos(θ_2),cos(θ_3)$ for the $x, y,z$ directions, respectively.

Then we know that,

The direction cosines satisfy the relation:

$cos^{2}θ_1 +cos^{2}θ_2+cos^{2}θ_3 = 1$

This is because the direction cosines form a unit vector in three-dimensional space, and the sum of the squares of the direction cosines is always equal to 1.

Therefore, the value of $cos^{2}θ_1 +cos^{2}θ_2+cos^{2}θ_3$ is also $1$. (_Ans)