The angle between the vectors A = 3i + 5j - 4k and B = -5i + 11j + 10k is:

Question

Question

Answer 1

Concept:

The angle θ between the two vectors A and B is given by:

cos θ = \(\rm \vec A\cdot\vec B\over|\vec A||\vec B|\)

Calculation:

Given A = 3i + 5j - 4k and B = -5i + 11j + 10k

Let the angle between them be θ

cos θ = \(\rm (3i+5j-4k)\cdot(-5i+11j+10k)\over\sqrt{(3)^2+(5)^2+(-4)^2} \times\sqrt{(5)^2+(11)^2+(10)^2}\)

cos θ = \(\rm (-15+55-40)\over\sqrt{50} \times\sqrt{246}\)

cos θ = 0

∴ θ = \(\boldsymbol{\pi\over2}\)