Given :
Two vectors :
[tex]v_1=-30i+bj+5k\\\\v_2=bi+2bj+bk\\\\[/tex]
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 ,
[tex]-30b+2b^2+5b=0\\\\2b^2-25b=0\\\\b(2b-25)=0[/tex]
Therefore , for b =0 and [tex]b=\dfrac{25}{2}[/tex] the vectors are orthogonal .
Hence , this is the required solution .
