Consider the planes `3x-6y-2z-15 =0` and `2x+y-2z - 5=0` Statement 1:The parametric equations 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 the line of intersection of the given planes. which of the statement is true?

Options

A. a. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. b. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. c. Statement 1 is true and Statement 2 is false.
D. d Statement 1 is false and Statement 2 is true.

Answer

d

Explanation

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.