CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q384 Marksline_intersection
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 38 (Three Dimensional Geometry)
A glass box has corners A=(1,2,3), B=(2,2,3), C=(2,4,3), D=(1,4,3), A′=(1,2,6), B′=(2,2,6), C′=(2,4,6), D′=(1,4,6).
Part (1) 1 Marks
Write the Cartesian equation of AC′.
Answer: x−1=(y−2)/2=(z−3)/3.
- Subtract A from C′ to get direction (1,2,3).
- Use this direction and base point A.
Part (2) 1 Marks
Write the Cartesian equation of A′C.
Answer: x−1=(y−2)/2=(z−6)/(−3).
- Subtract A′ from C to get (1,2,−3).
- Use base point A′ and that direction.
Part (3) 2 Marks
Show the diagonals AC′ and A′C intersect.
Answer: They intersect at (3/2,3,9/2).
- Parametrize them as (1+t,2+2t,3+3t) and (1+s,2+2s,6−3s).
- Matching the first and third coordinates gives t=s=1/2.
- Both give (3/2,3,9/2), so the diagonals intersect.
Part (4) 2 Marks
Find the point of intersection of AC′ and A′C.
Answer: (3/2,3,9/2).
- The midpoint of AC′ is ((1+2)/2,(2+4)/2,(3+6)/2).
- The midpoint of A′C has the same coordinates.
- Thus the common midpoint (3/2,3,9/2) is their intersection.