Let be a unit vector coplanar with and such that is perpendicular to

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let

\hat{c}

be a unit vector coplanar with

a = \hat{i} - \hat{j} + 2\hat{k}

and

b = 2\hat{i} - \hat{j} + \hat{k}

such that

\hat{c}

is perpendicular to

a

. If

P

be the projection of

\hat{c}

along

b

, where

P = \frac{\sqrt{11}}{k}

then find

k