MHT CET202526 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual
The line x-1 2 = y+2 -1 = z 1 intersects the XY plane and the YZ plane at points A and B respectively. The equation of line through the points A and B is
Options
- A[ r -( i -2 j +0 k )] (- i + 1 2 j - 1 2 k )= 0
- B[ r +( i -2 j +0 k )] (- i + 1 2 j + 1 2 k )= 0
- Cr =(- i -2 j +0 k )+ (- i + 1 2 j - 1 2 k )
- Dr =( i +2 j )+ (- i + 1 2 j - 1 2 k )
Correct answer
A. [ r -( i -2 j +0 k )] (- i + 1 2 j - 1 2 k )= 0
Step-by-step solution
Find the line through A and B , where A is the intersection of the line x-1 2 = y+2 -1 = z 1 with the XY plane ( z=0 ), and B is its intersection with the YZ plane ( x=0 ). Set z=0 and z 1 =0 in the parametric ratio, yielding x-1 2 =0 and y+2 -1 =0 . Thus, x=1 , y=-2 , and A is (1, -2, 0) . Set x=0 and denote 0-1 2 = - 1 2 . From y+2 -1 = - 1 2 , cross-multiplying gives y+2 = 1 2 , so y = - 3 2 . Similarly, z 1 = - 1 2 , so z = - 1 2 , and B is (0, - 3 2 , - 1 2 ) . The direction vector from A to B is b - a = (0-1)