SOLUTION: Find the vector projection of u onto v. Then write u as the sum of two orthogonal​ vectors, one of which is proj(Subscript v)u. u= <2​,8>, v=<4​,-5>

Algebra ->  Trigonometry-basics -> SOLUTION: Find the vector projection of u onto v. Then write u as the sum of two orthogonal​ vectors, one of which is proj(Subscript v)u. u= <2​,8>, v=<4​,-5>       Log On


   

Question 1132636: Find the vector projection of u onto v. Then write u as the sum of two orthogonal​ vectors, one of which is proj(Subscript v)u.
u= <2​,8>, v=<4​,-5>
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
u= <2​,8>, v=<4​,-5>
proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2*<4​,-5>

u%2Av=+8%E2%80%8B-40=-32
%28abs%28u%29%29%5E2=%28sqrt%284%5E2%2B5%5E2%29%29%5E2=%28sqrt%2841%29%29%5E2

substitute in proj%5Bv%5Du=%28u%2Av%29%2F%28abs%28u%29%29%5E2*<4​,-5>

proj%5Bv%5Du=-32%2F%28sqrt%2841%29%29%5E2*<4​,-5>

proj%5Bv%5Du=(-32%2F41)*<4%E2%80%8B,-5>

proj[v]u=(-32%2F41%294%E2%80%8B,(-32%2F41%29%28-5%29)

proj%5Bv%5Du=(-128%2F41​,160%2F41)