3D Geometry 3 Question 60

####60. Consider the planes 3x6y2z=15 and 2x+y2z=5.

Statement I The parametric equations of the line of intersection of the given planes are x=3+14t, y=1+2t,z=15t.

Statement II The vectors 14i^+2j^+15k^ is parallel to the line of intersection of the given planes.

(2007,3M)

Match the Columns

Match the conditions/expressions in Column I with values statements in Column II.

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Answer:

Correct Answer: 60. (d)

Solution:

  1. Given planes are 3x6y2z=15 and 2x+y2z=5.

For z=0, we get x=3,y=1

Since, direction ratios of planes are

<3,6,2> and <2,1,2>

Then the DR’s of line of intersection of planes is <14,2,15> and line is

x314=y+12=z015=λx=14λ+3,y=2λ1,z=15λ

Hence, Statement I is false.

But Statement II is true.



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