Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the value of $λ$ for which the line $2x−1 =3y−1 =λz−1 $ is parallel to the plane $r⋅(2i^+3j^ +4k^)=4$.

Clearly, the given line must be perpendicular to the normal to the given plane.

direction ratios of the given line are $2,3,λ$

direction ratios of the normal to the given plane are $2,3,4$.

$∴(2×2)+(3×3)+(λ×4)=0$

$⇒4λ=−13$

$⇒λ=4−13 $.