Calculus Vector

Question

Let a=<2,1,5> and b=<−5,2,k>.

Find K so A and B will be orthogonal

Answer 1

Hi Al,

When vectors are orthogonal, their dot product is equal to 0. This is because

a • b = |a||b|cos(θ), and orthogonal is 90°, meaning cos(90°) is 0 and the dot product is hence 0.

The dot product of the two vectors is (2)(-5) + (1)(2) + (5)(k) = 5k - 8,= 0, so k = 8/5.

Hope this helps!

Akshat Y.