Diketahui Vektor A =2i ̂+2j ̂-3k ̂ , dan

Posted on

vektor B =-2i ̂+3j ̂-4k ̂. Hitunglah!

A. Besar vektor A dan B

B. Besar |A×B|

Diketahui Vektor A =2i ̂+2j ̂-3k ̂ , dan

A = (2i, 2j, -3k)

B = (-2i, 3j, -4k)

~> |A| = √Ai² + Aj² + Ak²

= √4 + 4 + 9

= √17 satuan ✓✓

|B| = √4 + 9 + 16

= √29 satuan ✓✓

~> A × B = (2i, 2j, -3k) × (-2i, 3j, -4k)

= [- (4 i×i) + (6 i×j) – (8 i×k) – (4 j×i) + (6 j×j) – (8 j×k) + (6 k×i) – (9 k×j) + (12 k×k)]

= [0 + 6k + 8j + 4k + 0 – 8i + 6j + 9i + 0]

= [i, 14j, 10k] ✓

|A × B| = √1 + 196 + 100

= √297 satuan ✓✓