Question

If vector a = 5i - j - 3k and vector b = i + 3j - 5k, then show that the vectors a + b and vector(a - b) are perpendicular.

Answer 1

We know that two nonzero vectors are perpendicular if their scalar product is zero.

Here, vector(a + b) = 5i - j - 3k + i + 3j - 5k = 6i + 2j - 8k

and vector (a - b) = 5i - j - 3k - i - 3j + 5k = 4i - 4j + 2k

Now, vector(a + b) x vector (a - b) = (6i + 2j - 8k) x (4i - 4j + 2k) = 24 - 8 - 16 = 0

Hence vector(a + b) and vector (a - b) are perpendicular.