Question

Find the angle between the vectors A = 3i - 4j + 5k and B = i - j + k ?

Answer 1

Suppose vector A = 3i + 4j + 5k and

vector B = i + j + k

Now, mode A = √(3^2 + 4^2 + 5^2)

= 5*√(2)

And mode B = √( 1^2 + 1^2 + 1^2) = √(3)

Now ,A × B = i (4*1- 5*1) + j(5*1 - 3*1) + k(3*1 - 4*1) = - i + 2j - k

So,mode A×B = √((-1)^2 + (2)^2 + (-1)^2) = √(6)

If the angle between vectors A and B is X then sin X = ( mode A× B)/((mode A)*(mode B))

= √(6)/((5*(√(2))*(√(3))) = 1/5.