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Question

The distance of origin from the point of intersection of the line x2=y-23=z-34 and the plane 2x+y-z=2 is


A

120

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B

83

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C

219

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D

78

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Solution

The correct option is D

78


Explanation for the correct option:

Step-1 : Find the value of x,y and z

Given, the point of intersection is given by x2=y-23=x-34

Equation of the plane is 2x+y-z=21

Let, the points on this line bex2=y-23=x-34=t

Equating the above expression we get,

x=2t,y=3t+2,z=4t+3

Substituting the values of x,y,z in equation 1

2(2t)+3t+2-(4t+3)=2

4t+3t-4t-1=2

3t=3t=1

Substituting the value of t in the equations for x,y,z

x=2t=2×1=2y=3t+2=3×1+2=5z=4t+3=4×1+3=7

Thus the point is (2,5,7)

Step-2 :Find the distance of origin from the point of intersection.

Distance from origin=x2+y2+z2=22+52+72

=4+25+49

=78

Hence, option (D) is the correct answer.


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