For the following two (02) items: A plane P is parallel to the line having direction ratios 1, 3, 2 and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0. Which of the following are the direction ratios of the line of intersection of the given planes?
B. 2, -23, -16
The normal vectors of the given planes are n _1 = 6, 4, -5 and n _2 = 1, -2, 3 . The direction vector d of the line of intersection of the planes is given by the cross product of their normal vectors: d = n _1 n _2 = vmatrix i & j & k \\ 6 & 4 & -5 \\ 1 & -2 & 3 vmatrix d = i (12 - 10) - j (18 + 5) + k (-12 - 4) d = 2 i - 23 j - 16 k The direction ratios of the line of intersection are 2, -23, -16 . Answer: 2, -23, -16
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks