The line drawn $(4,-1,2)$ and $(-3,2,3)$ meets the plane at right angles at the point $(-10,5,4)$ then the…

The line drawn $(4,-1,2)$ and $(-3,2,3)$ meets the plane at right angles at the point $(-10,5,4)$ then the equation of plane is
  1. $2 x-y-z+29=0$
  2. $7 x-3 y-z+89=0$
  3. $x-y+z+11=0$
  4. $x+y+z+1=0$

Solution

d.r's of normal to the plane are $ < 4-(-3),-1-2$, $2-3>^0 < 7,-3,-1>$ and it passes through $(-10,5,4)$. Hence the required equation is $\begin{aligned} & 7(x-(-10))-3(y-5)-1(z-4)=0 \\ & \Rightarrow 7 x-3 y-z+89=0 \end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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