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Consider the following
A line L passes through the point P(5, - 6,7) and is parallel to the planes x + y + z = 1 and 2 x - y - 2 z = 3.
Q. What are the direction ratios of the line of intersection of the given planes?
  • a)
    < 1 , 4 , 3 >
  • b)
    < - 1 , - 4 , 3>
  • c)
    < 1 ,- 4 ,3>
  • d)
    < 1 ,- 4 ,- 3 >
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the followingA line L passes through the point P(5, - 6,7) an...
Let a, b, c be the direction ratios of the line.
Then its equation is
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Most Upvoted Answer
Consider the followingA line L passes through the point P(5, - 6,7) an...
To find the direction ratios of the line of intersection of the given planes, we first need to find the normal vectors of the planes.

For the plane x + y + z = 1, the normal vector is <1, 1,="" 1="">.
For the plane 2x - y - 2z = 3, the normal vector is <2, -1,="" -2="">.

The direction ratios of the line of intersection of the given planes will be the cross product of the normal vectors of the planes.

<1, 1,="" 1=""> x <2, -1,="" -2=""> = (1*(-2) - 1*(-2), -(1*2) - 1*(-2), 1*(-1) - 1*2)
= (-4 + 2, -2 + 2, -1 - 2)
= (-2, 0, -3)

Therefore, the direction ratios of the line of intersection of the given planes are -2, 0, -3.
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Consider the followingA line L passes through the point P(5, - 6,7) and is parallel to the planes x + y + z = 1 and 2 x - y - 2 z = 3.Q. What are the direction ratios of the line of intersection of the given planes?a)< 1 , 4 , 3 >b)< - 1 , - 4 , 3>c)< 1 ,- 4 ,3>d)< 1 ,- 4 ,- 3 >Correct answer is option 'C'. Can you explain this answer?
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