Home/ Questions/Q 426790
Next
In Process
Ehsaan Jani
Asked: 2022-11-09T18:31:27+05:30 In:

Consider the planes `3x-6y-2z=15a n d2x+y-2z=5.`Statement 1:The parametricequations of the line intersection of the given planes are `x=3+14 t ,y=2t ,z=15 tdot`Statement 2: The vector `14 hat i+2 hat j+15 hat k`is parallel to theline of intersection of the given planes.
A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.

Consider the planes `3x-6y-2z=15a n d2x+y-2z=5.`Statement 1:The parametricequations of the line intersection of the given planes are `x=3+14 t ,y=2t ,z=15 tdot`Statement 2: The vector `14 hat i+2 hat j+15 hat k`is parallel to theline of intersection of the given planes.
A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.
Parabola
Leave an answer

Leave an answer

Browse

1 Answer

  1. Correct Answer – d
    The line of intersection of the given plane is `3x-6y-2z-15=0= 2x+y-2z-5=0`
    For `z=0`, we obtain `x=3 and y=-1`.
    `therefore” “` Line passes through `(3, -1, 0)`
    Also, the line is parallel to the cross product of normal to given planes, that is
    `” “|{:(hati,,hatj,,hatk),(3,,-6,,-2),(2,,1,,-2):}|= 14hati+2hatj+15hatk`
    The equation of line is `(x-3)/(14)= (y+1)/(2)= (z)/(15) = t`,
    whose parametic form is
    `” “x=3+14t, y=-1+2t, z=15t`
    Therefore, Statement 1 is false.
    However, Statement 2 is true.

    • 0