Penjelasan dengan langkah-langkah:

1. AB = (4-3, 3+2, 3-2) = (1, 5, 1)

2. P = [(9+6)/5, (-9+4)/5, (21-6)/5] = (3, -1, 3)

PC = (-1-3, 6+1, 5-3) = (-4, 7, 2)

3. 3KL - MN = 2LN

3KL = MN + 2LN

3KL = N(M + 2L)

3(1, 0, 6) = N(4, 5, 4 + 2(4, 5, 7)

(3, 0, 18) = N(12, 15, 18)

N = (12-3, 15-0, 18-18)

N = (9, 15, 0)

4. R = [(24-6)/5 , (21-4)/5 , (24+6)/5]

R = (18/5 , 17/5 , 30/5)

5. r = (10-8, 6-3, -3-3)

r = 2i + 3j - 6k

6. a =PQ = (1, -3, -3)

b = RP = (0, 3, 0)

c = b - a

c = (-1, 6, 3)

7. (a.b) = |a||b| cos 60°

(a.b) = (4)(2)(½) = 4

a(a + b) = |a| + (a.b) = 8

8. PQ = (-1, 5, 1)

QR = (-1, -4, 4)

@ = PQ.QR/|QR|

@ = (1-20+4)/√(1+16+16)

@ = (-15)/√33

@ = (-5/11)√33