Question

For what values of a are v = a i − j + k and w = a i + a j − 3 k perpendicular? give exact values.

Answer 1

The vectors are perpendicular when their dot product is zero. That is
.. a^2 -a -3 = 0
.. (a -1/2)^2 -13/4 = 0
.. a = (1 ±√13)/2