SOLUTION: How do you Find the projection of u onto v. u = −5, −4 v = −8, −1 And my second question was, how do you write u as the sum of two orthogonal vectors, one of which is

Algebra ->  Trigonometry-basics -> SOLUTION: How do you Find the projection of u onto v. u = −5, −4 v = −8, −1 And my second question was, how do you write u as the sum of two orthogonal vectors, one of which is       Log On


   



Question 1206737: How do you Find the projection of u onto v.
u = −5, −4
v = −8, −1
And my second question was, how do you write u as the sum of two orthogonal vectors, one of which is proj v u?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The vector projection is given by
proj%5Bu%5D%28v%29=%28%28v%2Au%29%2Fu%5E2%29%2Au

vectors dot product u%2Av=%28-5%29%28-8%29%2B%28-4%29%28-1%29=40%2B4=44
magnitude of vector u=sqrt%28%28-8%29%5E2%2B%28-1%29%5E2%29=sqrt%2865%29

proj%5Bu%5D%28v%29=%2844%2F%28sqrt%2865%29%29%5E2%29*<-8,-1>

proj%5Bu%5D%28v%29=%2844%2F65%29*<-8,-1>....scalar multiplication is

proj%5Bu%5D%28v%29=<-8%2844%2F65%29,-1%2844%2F65%29)>

proj%5Bu%5D%28v%29=<-352%2F65,-44%2F65>

proj%5Bu%5D%28v%29 ≈<-5.415,-0.677>