Mathematics

Problem

Two points

P

and

Q

are given in the rectangular cartesian coordinates in the curve

y = 2^{x+2}

, such that

\mathbf{OP} \cdot \hat{i} = -1

and

\mathbf{OQ} \cdot \hat{i} = 2

, where

\hat{i}

is a unit vector along the

X

-axis. Find the magnitude of

\mathbf{OQ} - 4\mathbf{OP}