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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The equation of plane passing through the point $(0,7,-7)$ and containing the line
$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$
is:
Solution
The line
$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$
gives a point on the line
$(-1,3,-2)$
Direction vector of line
$\vec d=(-3,2,1)$
Vector joining given point and line point
$(0,7,-7)-(-1,3,-2)=(1,4,-5)$
Normal vector of plane
$\vec n = \vec d \times (1,4,-5)$
$\vec n=
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
-3 & 2 & 1 \\
1 & 4 & -5
\end{vmatrix}$
$= -14\mathbf{i}-14\mathbf{j}-14\mathbf{k}$
Normal vector $\propto (1,1,1)$
Plane equation
$x+y+z+d=0$
Substitute point $(0,7,-7)$
$0+7-7+d=0$
$d=0$
Plane
$x+y+z=0$
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