3D Geometry
Three Dimensional Geometry
star_batch_jee_advanced_2025
Grade 12

Question:

The value of $\sin^{-1} \sin \lambda$ is equal to:
3
$\pi - 3$
4
$\pi - 4$

Step-by-Step Solution

Key Concept: Lines are coplanar when the scalar triple product of a connecting vector and both direction vectors equals zero.
Two lines are coplanar if the determinant condition is satisfied. Setting up the determinant with direction and position vectors of both lines, we solve $2(2-3)+3(3+3)+\lambda(-3-2) = 0$, yielding $\lambda = 4$. With $\lambda = 4$, we verify using $\sin^{-1}\sin 4 = \sin^{-1}\sin(\pi-4) = \pi - 4$.
Correct Answer: 4

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