Pre Calculus

Question

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

a) -12/13i-60/13j

b) 1/13i+5/13j

c) 12/13i+60/13j

d) -1/13-60/13j

Answer 1

the coordinates of vector u are: (1,-5)

the coordinates of vector v are: (1,5)

 

u•v = u_i*v_i + u_j*v_j

u•v = 1*1 + (-5)*5 = 1 - 25 = -24

 

||v||² = (v_i)² + (v_j)²

||v||² = 1 + 25 = 26

 

Thus: proj_vu = ((u•v)/||v||²)v

proj_vu = -24/26 v

proj_vu = -12/13 * (i+5j)

proj_vu = -12/13i - 60/13j