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  4. If equation of plane passing through the point of intersection of lines (x-1/3)=(y-2/1)=(z-3/2) and (x-3/1)=(y-1/2)=(z-2/3) and at greatest distance from origin is 4 x+a y+b z=c, then find the value of (a+b+c)

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Q. If equation of plane passing through the point of intersection of lines $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and at greatest distance from origin is $4 x+a y+b z=c$, then find the value of $(a+b+c)$

Vector Algebra

Solution:

Point of intersection of the given lines is (4, 3, 5).
Required plane is through $(4,3,5)$ and perpendicular to line joing $(4,3,5) \&(0,0,0)$.
$\Rightarrow$ Equation of planes $4(x-4)+3(y-3)+5(z-5)=0$