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Find the distance of the point (2,3,4) f...

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`.

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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.
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RS AGGARWAL-THE PLANE-Exercise 28B
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  8. Find the coordinates of the image of the point P(1, 3, 4) in the plane...

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  9. Find the point where the line (x-1)/2=(y-2)/-3=(z+3)/4 meets the plane...

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  10. find the coordinates of point where the line through (3,-4,-5) and (2,...

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