NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the line x - 4 1 = y - 2 1 = z - m 2 lies in the plane 2 x + l y + z = 7, then the value of m + 2 l is equal to

Options

A1
B2
C- 1
D- 2

Correct answer

C. - 1

Step-by-step solution

A vector parallel to the line is i ^ + j ^ + 2 k ^ A vector normal to the plane is 2 i ^ + l j ^ + k ^ ∵ the line lies in the plane ⇒ 2 1 + 1 l + 2 1 = 0 ⇒ l = - 4 ∵ Point ( 4,2 , m ) also lies in the plane ⇒ 2 4 + l 2 + m = 7 ⇒   m = 7 Hence, m + 2 l = 7 - 8 = - 1

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