Question

Find the values of x such that the vectors [3,2,x\ and [2x, 4, x\ are orthogonal.

Answer 1

$(3,2,x)$ and $(2x,4,x)$ are orthogonal if their dot product is 0:

$(3,2,x)\cdot(2x,4,x)=6x+8+x^2=(x+3)^2-1=0\implies x=-3\pm1$

$\implies x=-4\text{ or }x=-2$