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Q.

The equation of a line 4x4yz+11=0=x+2yz1 can be put as: 

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a

x2=y21=z34 and x42=y42=z112

b

x22=y1=z34

c

x42=y42=z112

d

x22=y21=z4

answer is A.

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Detailed Solution

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The given equation are

4x4yz+11=0       ….(i)

x+2yz+1=0           …. (ii)

The DR's of normals to the planes (i) and (ii) are 4,-4,-1 and 1,2,-1 respectively.

Let DR's ofline of intersection of plane be l.m.n As the line of intersection of the planes is perpendicular to 

the normals of the both planes, we get 4l4mn=0 and l+2mn=0

By cross multiplication l6=m3=n12

or l2=m1=n4

If x = 0, equation (i) and (ii) becomes 4yz+11=02yz1=0

Solving, we get y=2,z=3

Equation o me is x2=y21=z34

Also x=4,y=4,z=11 satisfies equation (i) and (ii) Hence, (b) is also the correct option. 

 

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