Question

if u=-4i+6J and v=-i+5j and w=-3i+9j find proj u

Answer 1

Unit vector for v=v̂=v/|v|=(-i+5j)/√26.

Unit vector for u=û=u/|u|=(-4i+6j)/√52.

cosα=û.v̂, where α is the angle between the unit vectors,

cosα=(4+30)/(26√2)=17√2/26.

Projection of u onto v=(17√2/26)|u|=(17√2/26)√52=17√26/13=6.6679 approx.

Unit vector for w=ŵ=w/|w|=(-3i+9j)/√90.

cosβ=(12+54)/(6√130)=11/√130,

projection of u onto w=(11/√130)√52=11√(52/130)=11√⅖=6.9570 approx.