If the vectors p i+ j+ k, i+q j+ k and i+ j+r k (p q r 1) are coplanar, then the value of …

Question

If the vectors $p\hat i+\hat j+\hat k$, $\hat i+q\hat j+\hat k$ and $\hat i+\hat j+r\hat k$ ($p
e q
e r
e 1$) are coplanar, then the value of $pqr-(p+q+r)$ is:

Accepted Answer

$$\begin{vmatrix}p&1&1\1&q&1\1&1&r\end{vmatrix}=0 \implies p(qr-1)-(r-1)+(1-q)=0 \implies pqr-(p+q+r)+2=0$$

$pqr-(p+q+r)=-2$

Solutions · 1