Question

Determine the value of n so that the vectors A and B are perpendicular: Ā = î + 5j + nk and B = 2î - j + k

Answer 1

If $\vec A$ and $\vec B$ are perpendicular, then their dot product is zero. This means

$\vec A \cdot \vec B = (\vec\imath + 5\,\vec\jmath + n\,\vec k) \cdot (2\,\vec\imath - \vec\jmath + \vec k) = 2 - 5 + n = 0$

Solving for n is trivial; it follows that n = 3.