Question

Let a and b be real numbers. Find all vectors left angle 1 comma a comma b right angle orthogonal to left angle 1 comma 8 comma 1 right angle.

Answer 1

`A = (1, a, -1-8a)`. a and b are reals numbers.

Explanation:

Let the vectors A = (1, a, b) and B = (1, 8, 1). If we assume that A and B are orthogonal vectors, then the scalar product between a and B is zero. Thus:

`A \bullet B = (1, a, b) \bullet (1, 8, 1) = 1 + 8a + b = 0\\b = - 1 - 8a`

All vectors A orthogonal to vector B = (1, 8, 1) are given by:
`A = (1, a, -1-8a)`. a and b are reals numbers.