Question

Calculate the scalar product of the following vectors.
Given three vectors a, b, and c. Prove that the vector $(b.c)a-(a.c)b$ is perpendicular to the vector c.

Answer 1

Two vectors are said to be perpendicular if their scalar product amounts to 0. To ascertain whether the given vector is perpendicular to c, we take its scalar product with $c$.

$\left(\right(b.c)a-(a.c\left)b\right).c$

$=\left(\right(b.c\left)a\right).c-\left(\right(a.c\left)b\right).c)$

$=(b.c)(a.c)-(a.c)(b.c)$

$=0$

Hence the vector $(b.c)a-(a.c)b$ is perpendicular to the vector $c$.