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Question

The coordinate of the point of intersection of the line [x-1]1=[y+2]3=[z-2]-2 with the plane 3x+4y+5z-25=0 is


A

(5,10,6)

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B

(10,5,6)

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C

(5,5,-6)

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D

(5,10,-6)

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Solution

The correct option is D

(5,10,-6)


Explanation for the correct option:

Finding the point of intersection

Given equation of line,

[x-1]1=[y+2]3=[z-2]-2

And equation of plane

3x+4y+5z-25=0...(i)

Now consider,

[x-1]1=[y+2]3=[z-2]-2=r

x=r+1,y=3r2,z=2r+2...(ii)

Substituting these values of x,y&z in (i)

3(r+1)+4(3r2)+5(-2r+2)25=05r20=0r=205r=4

Therefore, from (ii)

x=5,y=10,z=6

Thus the required point is (5,10,6)

Hence, option (D) is the correct answer.


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