Vector A and four other vectors that have the same magnitude but differ in orientation. a) Which of those other four vectors have the same dot product with A? b) Which have a negative dot product with A?
(Those circle things between the arrows are supposed to be thetas. I suck at drawing quickies in paint.)
a*b = abcos(theta)
The Attempt at a Solution
For a) I recognized that they would all have the same dot product with a, since the magnitude of all the vectors are the same, as is their angle. What I don't get is the answer to b. It says D and E. Shouldn't the dot products all be positive? In the equation a and b are positive (and always will be), and cos(theta) is positive in this case, how would the dot product turn out to be negative?
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