Question

Two vectors 5i + 7j -3k and 2i + 2j - ak are mutually perpendicular. What is the value of a?

Answer 1

$a = 12$

Explanation:

$we \: \: know \: \: \boxed{if \: \: \vec{a} \perp \vec{b} \: \: then \: \: \vec{a} . \vec{b} = 0} \\ \therefore \: \: \: (5i + 7j - 3k).(2i + 2j - ak) = 0 \\ 5 \times 2 + 7 \times 2 - 2 \times a = 0 \\ 10 + 14 - 2a = 0 \\ 24 - 2a = 0 \\ 2a = 24 \\ \boxed{a = 12}$