# Given that A = i+ a j + k and B = a i+ j + k, if A and B are normal to each other, what is a?

Jun 27, 2016

$a = - \frac{1}{2}$.

#### Explanation:

The sufficient condition for perpendicularity is the dot (scalar)

product

$A . B = \left(1\right) \left(a\right) + \left(a\right) \left(1\right) + \left(1\right) \left(1\right) = 2 a + 1 = 0$

So, $a = - \frac{1}{2}$.