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Questions  

Equation of the line passing through the point  1,2,3and perpendicular to the plane2x+3y+z+5=0

a
x−1−1=y+21=z−3−1
b
x+1−1=y−21=z+31
c
x+12=y−23=z+31
d
x+y−3=y−12=z−31

detailed solution

Correct option is C

The direction ratios of any line perpendicular to the plane  ax+by+cz+d=0are proportional toa,b,cThe equation of the line passing through the point  x1,y1,z1and parallel to the line whose direction ratios are a,b,cisx−x1a=y−y1b=z−z1cHence, the equation of the line passing through the point   −1,2,−3and perpendicular to the plane  2x+3y+z+5=0is  x+12=y−23=z+31

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