Q-the-non-zero-vector-a-a-1-a-2-a-3-with-the-coordinate-axes-makes-the-angles-and-prove-that-the-following-eq

Question Number 188881 by mnjuly1970 last updated on 08/Mar/23

Q : the non - zero vector \vec{a} = (a_{1}, a_{2}, a_{3}) with

the coordinate axes makes the

angles, α, β and γ . prove

that the following equality .

\cos^{2} (α) + \cos^{2} (β) + \cos^{2} (γ) = 1

Answered by mr W last updated on 08/Mar/23

d = \sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}

\Rightarrow \cos α = \frac{a_{1}}{d}

\Rightarrow \cos β = \frac{a_{2}}{d}

\Rightarrow \cos γ = \frac{a_{3}}{d}

\cos^{2} α + \cos^{2} β + \cos^{2} γ = \frac{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}{d^{2}} = 1

Commented by mnjuly1970 last updated on 08/Mar/23

t h a n k s a l o t s i r W