Pre Calculus

Question

Find the projection of vector u onto vector v; proj_vu=(u(times)v)/llvll²)v
u = 4i –5j and v = 2i + j .


a)-6/5i-3/5j

b)-26/5i-13/5j

c)26/5i+13/5j

d)6/5i+3/5j

 

Answer 1

"u(times)v" is the dot product = 4 * 2 + (-5) * 1 =  8 + -5 = 3

||v||² is the sum of the squares of the v components

     = 2² + 1² = 5

So proj_vu = ( 3 / 5) (2i + j) = 6/5 i + 3/5 j  .