Question

Which of the following vectors are orthogonal to (2,1)? More than 1 answer

A. (1,2)
B. (-3,6)
C. (-2,-3)
D. (1,-2)

Answer 1

Two vectors are orthogonal if they have an inner product of zero. So, take the inner product of (2,1) with each vector in the options, and see which ones evaluate to zero. Example: for A, we take the inner product of (2,1) with (1,2), which gives us \(2\cdot1+1\cdot2=4\ne0\), so A is not orthogonal.

Answer 2

so that means b c d?

Answer 3

Not all three of those have inner products of zero, no.

Answer 4

i thought it was a and d

Answer 5

if its orthogonal the dot product of the 2 vectors must equal to zero so:

the dot product is defined by:
v . u = < v1 , v2 > . <u1 , u2> = v1 u1 + v2 u2



b) and d)