Question

Calculate the scalar product of the following vectors.
For what value of $\alpha$ are the vectors $\{1,\alpha ,-2\}andb=\{\alpha ,3,-4\}$ mutually perpendicular?

Answer 1

We know that scalar product of two mutually perpendicular vectors is always 'zero'

$a.b=(\overrightarrow{i}+\alpha \overrightarrow{j}-2\overrightarrow{k}).(\alpha \overrightarrow{i}+3\overrightarrow{j}-4\overrightarrow{k})=0\Rightarrow \alpha +3\alpha +8=0$

$4\alpha =-8$

$\alpha =-2$ for a and b to be mutually perpendicular