Texts: Suppose x = -1, y = -3, z = -1. Then the vector (-5, 4, 0) is perpendicular to the vector (2, 6, 2) and the vector (4, 1, -7) is parallel to the vector (0, -1, -5). The vector (-4, 6, -5) is neither perpendicular nor parallel to the vectors given.
Suppose u = -4, v = 6, w = -5. Mark each vector below with a "T" if it is perpendicular to (u, v, w) and an "F" if it is not perpendicular to (u, v, w):
1. (3, 2, 0) - T
2. (11, -26, -40) - F
3. (-1, 1, 3) - T
4. (-5, 3, 1) - F
Find the norm of (u, v, w) and the unit vector in the direction of (3, -i):
|| (u, v, w) || = sqrt((-4)^2 + 6^2 + (-5)^2) = sqrt(16 + 36 + 25) = sqrt(77)
The unit vector in the direction of (3, -i) is (3, -i) / || (3, -i) ||.