The distance of the point (7, -3, -4) from the plane passing through the points (2, -3, 1), (-1, 1, -2) and (3, -4, 2) is :
Solutions · 1
Official solution
A(2,−3,1),B(−1,1,−2),C(3,−4,2)
\[
\begin{aligned}
& \overrightarrow{A B}=-3 \hat{i}+4 \hat{j}-3 \hat{k} \quad \overrightarrow{A C}=\hat{i}-\hat{j}+\hat{k} \\\\
& \vec{n}=\left|\[\begin{array}{|ccccccc|}\hat{i} & \hat{j} & \hat{k} \\ \\ -3 & 4 & -3 \\ \\ 1 & -1 & 1\end{array}\end{aligned}\]\right|=\hat{i}-\hat{k}
\]
Let equation of plane is x−z+λ=0 passes through point A(2,−3,1)⇒λ=−1
Equation of plane is x−z−1=0
Distance of point (7,−3,−4) from the plane x−z−1=0 is 52