Question

Calculate the scalar product of the following vectors.
For what values of x are the vectors $a=\{x,3,4\}andb=\{5,6,3\}$ perpendicular?

Answer 1

If a and b are two mutually perpendicular vectors then a.b=0

$a.b=(x\overrightarrow{i}+3\overrightarrow{j}+4\overrightarrow{k}).(5\overrightarrow{i}+6\overrightarrow{j}+3\overrightarrow{k})=0$

$5x+18+12=0$

$x=-6$