If the angle θ between the line $fraction numerator straight x plus 1 over denominator 1 end fraction space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 2 end fraction$ and the plane $space 2 straight x minus space straight y plus space square root of straight lambda space straight z space plus 4 space equals 0$ is such of sin θ = 1/3 the value of λ is

5/3

-3/5

3/4

-4/3

Solution

5/3

Angle between line and normal to plane is
$cos space open parentheses straight pi over 2 minus straight theta close parentheses space equals space fraction numerator 2 minus 2 space plus space 2 square root of straight lambda over denominator 3 space straight x square root of 5 space plus straight lambda end root end fraction$ where θ is the angle between line & plane
$rightwards double arrow space sin space straight theta space equals space fraction numerator 2 space square root of straight lambda over denominator 3 square root of 5 plus straight lambda end root end fraction space equals space 1 third straight lambda space equals space 5 over 3$

For Daily Free Study Material Join wiredfaculty

Three Dimensional Geometry

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction