Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 09/Solution 1

The two vectors $v$ and $x$ are perpendicular exactly when their dot product is zero. That is, when

$a+2a+3a+4a=0$

This condition simplifies to

$(1+2+3+4)a=10a=0$

Because the only solution to the above equation is $a=0$, there are no non-zero solutions to this problem.

Answer: $\color {blue}DNE$.