In triangle ABC, D is the midpoint of side BC. If vector AB + vector AC = K * vector AD, find K.

Correct answer: 2

Solution

Taking A as origin, position vectors of B and C are b and c. Then AB = b, AC = c, and AD = (b+c)/2 (midpoint). So AB + AC = b + c = 2*(b+c)/2 = 2*AD. Thus K = 2.

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