Given an equilateral with side length equal to

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Given an equilateral

\triangle ABC

with side length equal to

a

. Let

M

and

N

be two points respectively, on the side

AB

and

AC

such that

AN = kAC

and

AM = \frac{AB}{3}

. If

\mathbf{BN}

and

\mathbf{CM}

are orthogonal, then the value of

k

is (1)

\frac{1}{5}

(2)

\frac{1}{4}

(3)

\frac{1}{3}

(4)

\frac{1}{2}