Let u and v be two vectors in R2 whose Euclidean norms satisfy |u| = 2|v|. What is the value α such that w = u + αv bisects the angle between u and v ?
(A) 2
(B) 1/2
(C) 1
(D) -1/2
Answer: (A)
Explanation: |u| = 2|v| =|2v|. So u and 2v are vectors of the same length in directions of u and v, so their sum u+2v bisects the angle.
w = u + αv = u + 2 v
That is α = 2
Because, If we have two vectors with equal magnitude in the direction of given vectors, then their sum will
bisect the angle between them.
This explanation is contributed by Mithlesh Upadhyay.
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