Answer:
Step-by-step explanation:
Given the vectors u = (1, −1, −2) and v = (1, 1, 2),
projection of u on v is expressed as [tex]proj_v u = \dfrac{u*v}{|v|^2}*v[/tex]
u.v = (1, −1, −2).(1, 1, 2)
u.v = 1(1)+(-1)(1)+(-2)(2)
u.v = 1-1-4
u.v = -4
|v| = √1²+1²+ 2²
|v| = √1+1+4
|v| = √6
|v|² = (√6)²
|v|² = 6
[tex]proj_v u = \dfrac{-4}{6}*(1,1,2)\\proj_v u = (\dfrac{-4}{6}, \dfrac{-4}{6}, \dfrac{-4}{3} )[/tex]
Similarly for projection of v on u;
[tex]proj_u v = \dfrac{u*v}{|u|^2}*u[/tex]
|u| = √1²+(-1)²+ (-2)²
|u| = √1+1+4
|u| = √6
|u|² = (√6)²
|u|² = 6
[tex]proj_u v = \dfrac{-4}{6}*(1,-1,-2)\\proj_u v = (\dfrac{-4}{6}, \dfrac{4}{6}, \dfrac{4}{3} )[/tex]
