1.

Find the ratio in which the join the `A(2,1,5)a n dB(3,4,3)`is divided by the plane `2x+2y-2z=1.`Also, find the coordinates of the point ofdivision.

Answer» Suppose the given plnae intesects AB at a point C and let the required ratior be `lambda:1`
Then, the coordinates of C are
`((3lambda+2)/(lambda+1),(4lambda+1)/(lambda+1),(3lambda+5)/(lambda+1))`
Since C lies on the plane `2x+2y-2z=1`, this point must satisfy tyhe equation of the plane.
`:. 2((3lambda+2)/(lambda+1))+2((4lambda+1)/(lambda+1))-2((3lambda+5)/(lambda+1))=1 or lambda=(5)/(7)`
So, the required ratio is `(5)/(7) :1 , i.e., 5:7`
Putting `lambda=(5)/(j7)` in (i), then required point of division is `C((29)/(12),(9)/(4),(25)/(6))`


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