Kindly solve this using coordinate geometry?

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1 Answer
Jan 31, 2018

n=3

Explanation:

We know that

norm(B-A)^2 = normA^2+normB^2-2 normA norm B cos theta

and also

norm(B-A)-norm(A) = normB-norm(B-A) or

2norm(B-A) = normA+normB

and after substitution

costheta= (normA^2+normB^2-norm(B-A)^2)/(2 normA norm B ) =3/8(norm(A)^2+norm(B)^2)/(normA norm B)-1/4

Now making normB = lambda norm A

cos theta = 3/8(1+lambda^2)/lambda -1/4 which has a minimum at lambda = 1 giving cos theta = 1/2 and then

theta = pi/3

then, the value of n is 3.

Concluding, OAB is an equilateral triangle.