Question

What are the resultants of the vector product of two given vectors given by
A = 4i - 2j + k and B = 5i + 3j - 4k?

Answer 1

if two vectors A = a₁i + a₂j + a₃k and B = b₁i + b₂j + c₃k are given then,
A × B = (a₂b₃ - a₃b₂)i - (a₁b₃ - b₁a₃)j + (a₁b₂ - a₂b₁)k

Here given, A = 4i - 2j + k
B = 5i + 3j - 4k
A × B = (-2 × -4 - 1 × 3)i - (4 × -4 - 1 × 5)j + (4 × 3 - 5 × -2)k
= (8 - 3)i - (-16 - 5)j + (12 + 10)k
= 5i + 21j + 22j

Hence, Resultant of vector product of A and B = 5i + 21j + 22k