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 parame

1.	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.
Answer» 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.