# Once upon a time on a plane, there lived three vectors...

There are thee vectors \( \vec{a}, \vec{b}, \vec{c} \)

Given that \( \vec{a} = p\hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} + q\hat{j} + \hat{k} \) and \( \vec{c} = \hat{i} + \hat{j} + r\hat{k} \)

Given that these three vectors are **coplanar** and \( p \neq q \neq r \neq 1 \)

Then let the value of \( pqr - ( p+q+r) \) be \( k - 10 \)

Find **K**