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.
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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.
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.
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.