Question

if a=-2i+2j-k &b=3i+6j+2k then determined the angles between A&b

Answer 1

| a | = √ ( (-2)² + 2² + (-1)²) = √ (4+4+1) = 3
| b | = √ ( 3² + 6² + 2²) = √ (9+36+4) = 7

(a*b) = (-2)*3+2*6+(-1)*2 = -6 +12 -2 = 4

cos φ = (a*b) / (|a|*|b|) = 4 / (3*7) = 4/27     or    79°

Answer 2

A = -2i + 2j - k
B = 3i + 6j + 2k

|A| = sqrt(4 + 4 + 1) = 3
|B| = sqrt(9 + 36 + 4) = 7

A · B = (-2i + 2j - k) · (3i + 6j + 2k)
= -6 + 12 - 2
= 4

cosθ = A · B / ( |A| |B| )
= 4 / (3 × 7)
= 4 / 21

θ = cos⁻¹ (4/21)

Angle between A and B is cos⁻¹ (4/21)