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What is the dot product of r = (6, 0)^T with s = (0, 8)^T?

Answer:

(6, 0)^T · (0, 8)^T = 6*0 + 0*8 = 0

Same Vectors, Rotated

two vectors at right angles

The question was a particularly easy case. Here are the same two vectors rotated 45° :

r' = ( 6cos(45), 6sin(45) )^T
s' = ( -8sin(45), 8cos(45) )^T

Don't worry about how the vectors were rotated. This topic will come up soon enough.

QUESTION 8:

Form the dot product of the two vectors:

r' = ( 2cos(45), 2sin(45) )
s' = ( -3sin(45), 3cos(45) )

(Yes, I know, this looks awful. But it isn't. Just do it.)