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Question

A line is perpendicular to the plane x+2y+2z=0 and passes through (0,1,0). The perpendicular distance of this line from the origin is

A
53
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B
73
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C
23
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D
3
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Solution

The correct option is A 53
Since the line is perpendicular to the plane x+2y+2z=0, so directon of line will be (1,2,2) and it passes through (0,1,0),
Therefore equation of line is x1=y12=z2
So general point on the line is (r,2r+1,2r)
Now direction ratio of line passing through this point and origin which perpendicular to given line is (r,2r+1,2r)
Since they are perpendicular, so dot product will be 0 .
r+2×(2r+1)+2×2r=0
r+4r+2+4r=0
r=29
So points on line which perpendicular from origin is (2/9,5/9,4/9)
Now applying distance formula,
= (2/9)2+(5/9)2+(4/9)2
= 4/81+25/81+16/81
= 53

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