Determine if the vectors u 4upsilon and 2u upsilon are ort

Determine if the vectors u + 4upsilon and -2u - upsilon are orthogonal.

Solution

To check whether the vectors are orthoginal or not we find the dot product of the two vectors. If the dot product is zero then the vectors are orthogonal otherwise not. So lets us find the dot product of the given vectors.

(u+4v) (-2u-v)

= (1* -2) + (4*-1)

= -2 -4

= -6

Since we got the dot product = -6 which is not equal to 0.

Hence u+4v and -2u-v are not orthogonal.