Find a non zero- vector orthogonal to (1, 2, -1)

Answer 1

A vector that is orthogonal (perpendicular) to (1, 2, -1) must satisfy the condition that its dot product with (1, 2, -1) is zero. Let's call this unknown vector (a, b, c), so we need to solve the equation:

(1, 2, -1) dot (a, b, c) = 0

This means:

1a + 2b - 1c = 0

We can choose any values for a and b, and then solve for c. For example, let's choose a=1 and b=0:

1(1) + 2(0) - 1c = 0
c = 1

So one possible vector orthogonal to (1, 2, -1) is (1, 0, 1).

Note that there are infinitely many vectors orthogonal to any given vector, since we could also choose different values for a and b and get different solutions for c.