Aspire Faculty ID #17313 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

A ball is thrown upwards from the plane surface of the ground.  
Suppose the plane surface from which the ball is thrown consists of the points  

$A(1,0,2),\; B(3,-1,1)$ and $C(1,2,1)$ on it.  

The highest point of the ball takes is $D(2,3,1)$ as shown in the figure.

Using this information answer the question.

Solution

Points  

$A(1,0,2)$  
$B(3,-1,1)$  
$C(1,2,1)$

Direction vectors

$\vec{AB}=(3-1,-1-0,1-2)=(2,-1,-1)$

$\vec{AC}=(1-1,2-0,1-2)=(0,2,-1)$


Normal vector of plane

$\vec{n}=\vec{AB}\times\vec{AC}$


$\vec{n}=
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k}\\
2 & -1 & -1\\
0 & 2 & -1
\end{vmatrix}$


$=3\mathbf{i}+2\mathbf{j}+4\mathbf{k}$


So normal vector

$(3,2,4)$


Equation of plane

$3(x-1)+2(y-0)+4(z-2)=0$


$3x+2y+4z-11=0$


$3x+2y+4z=11$
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