Mathematics

Mathematics

Problem

Let two non-collinear vectors

\mathbf{a}

and

\mathbf{b}

inclined at an angle

\frac{2\pi}{3}

be such that

|\mathbf{a}| = 3

and

|\mathbf{b}| = 2

. If a point

P

moves so that at any time

t

its position vector

\mathbf{OP}

(where

O

is the origin) is given as

\mathbf{OP} = \left(t + \frac{1}{t}\right)\mathbf{a} + \left(t - \frac{1}{t}\right)\mathbf{b}

, then least distance of

P

from the origin is a.

\sqrt{2\sqrt{133} - 10}

b.

\sqrt{2\sqrt{133} + 10}

c.

\sqrt{5 + \sqrt{133}}

d.

\text{None of these}

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