Find the value of k for which the vectors 3 3 1 1 and 5 1

Find the value of k for which the vectors [-3 - 3 - 1 1] and [- 5 1 5 k] are orthogonal.

Solution

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Please note that two vectors are orthogonal if their dot product is equal to 0

For the given set of vectors

(-3).(-5) + (-3)(1) + (-1)(5) + (1)(k) = 0

15 -3 -5 + k =0

k = -7

Solution