Find the values of $x$ such that the vectors $( 2 x , x , 5 )$ and $( 4 , x , 3 )$ are orthogonal. Select the correct answer.
A) $x = - 5 , x = - 3$
B) $x = 5 , x = - 5$
C) $x = - 5 , x = 3$
D) $x = 3 , x = - 3$
E) $x = 5 , x = 3$

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero. So, we have:$$(2x, x, 5) \cdot (4, x, 3) = 0$$$$8x + x^2 + 15 = 0$$$$x^2 + 8x + 15 = 0$$$$(x + 3)(x + 5) = 0$$$$x = -3, -5$$

Find the Values Of xxx Such That the Vectors (2x,x,5)( 2 x , x , 5 )(2x,x,5)

Find the Values Of $x$ Such That the Vectors $( 2 x , x , 5 )$