Find all values for a such that v vector alpha 5 2 and w ve

Find all values for a such that v vector = (alpha 5 2) and w vector = (alpha alpha 3) are orthogonal.

Solution

v and w are orthogonal
so there dot product must be 0
(v).(w) = 0
a^2 + 5*a + 6 = 0
a^2 + 3*a + 2*a + 6 = 0
(a+3)(a+2)=0
a=-3 and a=-2

Answer:
a can be -3 or -2