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

Answer 1

To find a vector orthogonal to a given vector, we can take the cross product of the given vector with any arbitrary vector. Let's choose the vector (1, 0, 0) as our arbitrary vector.

The cross product of vectors (a, b, c) and (x, y, z) is given by:
(a, b, c) × (x, y, z) = (bz - cy, cx - az, ay - bx)

Using this formula, we can calculate the cross product of (1, 2, -1) and (1, 0, 0):
(1, 2, -1) × (1, 0, 0) = (2(0) - (-1)(0), (-1)(1) - 1(0), 1(0) - 2(1))
= (0, -1, -2)

Therefore, the vector (0, -1, -2) is orthogonal to (1, 2, -1).