Question

For what values of b are the given vectors orthogonal? (−30, b, 5), (b, b2, b)

Answer 1

Given :

Two vectors :

$v_1=-30i+bj+5k\\\\v_2=bi+2bj+bk$

To Find :

The value of b for which the vectors are orthogonal .

Solution :

We know , two vectors are orthogonal when the are perpendicular to each other .

So , their dot product will be zero .

So ,

$-30b+2b^2+5b=0\\\\2b^2-25b=0\\\\b(2b-25)=0$

Therefore , for b =0 and $b=\dfrac{25}{2}$ the vectors are orthogonal .

Hence , this is the required solution .