Find the distance of the point (2,3,4) from the plane `3x+2y+2z+5=0` measured parallel to the line `(x+3)/3=(y-2)/6=z/2`.

Find the distance of the point (2,3,4) from the plane `3x+2y+2z+5=0` m

1.	Find the distance of the point (2,3,4) from the plane `3x+2y+2z+5=0` measured parallel to the line `(x+3)/3=(y-2)/6=z/2`.
Answer» Equation of a line through A(2,3,4) and parallel to the given line is `(x-2)/3=(y-3)/6=(z-4)/2=lambda` (say). A general point on line (i) is `N(3lambda+2,6lambda+3,2lambda+4)`. For some value of `lambda`, it lies on the plane `3x+2y+2z=5`. `therefore 3(3lambda+2)+2(2lambda+4)+5 =0 rArr 25lambda=-25 rArr lambda=-1`. `therefore` the coordinates of N are `(-3+2,-6+3,-2+4)`, i.e.,`(-1,-3,2)`. Now, find AN=7 units.

Find the equation of a line passing through the point `(2hati-3hatj-5hatk)` and perpendicular to the plane`vecr.(6hati-3hatj+5hatk) +2=0`. Also find the point of intersection of this line and the plane.
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Find the coordinates of the image of the point P`(1, 3, 4)` in the plane `2x-y+z+3=0`.
Find the equationof the plane passing through each group of points. i) A(2,2,-1), B(3,4,2) and C(7,0,6) ii) A(0,-1,-1), B(4,5,1) and C(3,9,4) iii) A(-2,6,-6), B(-3,10,-9) and C(-5,0,-6).
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Find the distance of the point `(-1,-5,-10)` from the point of the intersection of the line `vecr = 2hati-2hatk+lambda(3hati+4hatj+2hatk)` and the plane `vecr.(hati-hatj+hatk) = 5`.
Find the distance of the point `(2hati-hatj-4hatk)` from the plane `vecr.(3hati-4hatj+12hatk)=9`.