Find the values of $x$ such that the vectors $( 2 x , x , 9 )$ and $( 6 , x , 3 )$ are orthogonal. Select the correct answer.
A) $x = 9 , x = 3$
B) $x = 3 , x = - 3$
C) $x = 9 , x = - 9$
D) $x = - 9 , x = 3$
E) $x = - 9 , x = - 3$

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero. The dot product of $(2x, x, 9)$ and $(6, x, 3)$ is $12x + x^2 + 27$. Setting this equal to zero gives the quadratic equation $x^2 + 12x + 27 = 0$, which factors to $(x + 9)(x + 3) = 0$. Thus, $x = -9$ or $x = -3$.

Find the Values Of xxx Such That the Vectors (2x,x,9)( 2 x , x , 9 )(2x,x,9)

Find the Values Of $x$ Such That the Vectors $( 2 x , x , 9 )$