Question

Find the value of k for which the vectors [-2, 1, 5, 2] and [4, -5, 4, k] are orthogonal. a) k = 6 b) k = -6 c) k = 0 d) k = 2

Answer 1

To find the value of k for which the vectors [-2, 1, 5, 2] and [4, -5, 4, k] are orthogonal, set up a dot product equation and solve for k.

Step-by-step explanation:

To find the value of k for which the vectors [-2, 1, 5, 2] and [4, -5, 4, k] are orthogonal, we need to determine when their dot product is equal to zero.

The dot product of the two vectors can be calculated by multiplying corresponding elements and summing the results:

[-2 * 4 + 1 * (-5) + 5 * 4 + 2 * k] = 0

Simplifying the equation gives: -8 - 5 + 20 + 2k = 0.

Combining like terms gives: 2k + 7 = 0.

Solving for k, we get k = -3.5.

Therefore, the correct value of k is -3.5.