write MN as the sum of unit vectors for M(-3/4, 5, 2/3) and N(6, -9, 3/5).

Question

Someone help me please?

Answer 1

vector MN = [6+3/4 , -9-5 , 3/5-2/3]
= [ 27/4 , - 14 , -1/15]

magnitude of MN = √(729/16+ 196 + 1/225)
= √(870354/3600)
= appr. 15.549

so a unit vector in the direction of MN
= 1/15.549 [27/4, -14, -1/15]
= [ .434 , -.900 , -.004]

check: .434^2 + (-.9)^2 + (.004)^2 = .99918 (very close to 1, that's good)

so [ .434 , -.900 , -.004]
= .434[1,0,0] - .9[0,1,0] - .004[0,0,1]

Answer 2

Thank you so much for providing a clear explanation!! :)