The-projection-of-the-vector-a-4i-3j-2k-on-the-axis-making-equal-acute-angles-with-the-coordinate-axes-is-

Question Number 54418 by gunawan last updated on 03/Feb/19

The projection of the vector a = 4 i - 3 j + 2 k

on the axis making equal acute angles

with the coordinate axes is

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19

a = 4 i - 3 j + 2 k s o ∣ a ∣= \sqrt{4^{2} + {(- 3)}^{2} + {(2)}^{2}} = \sqrt{29}

p r o j e c t i o n a l o n g x a x i s = i \sqrt{29} c o s α =

a l o n g y a x u s = j \sqrt{29} c o s β

a l o n g z a x i s = k \sqrt{29} c o s γ

{c o s}^{} α = c o s β = c o s γ = l

l^{2} + l^{2} + l^{2} = 1 s o l = \pm \frac{1}{\sqrt{3}}

s o p r o j e c t i o n a l o n g x a x u s = \pm \frac{\sqrt{29}}{\sqrt{3}} i

p r o j e c t i o n a l o n g y a x i s = \pm \frac{\sqrt{29}}{\sqrt{3}} j

p r o j e c t i o n z a x i s = \pm \frac{\sqrt{29}}{\sqrt{3}} k

o t h e r s p l s c h e c k \dots