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

Level pending

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

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