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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the plane a x - b y + c z = d contains the line x - a a = y - 2 d b = z - c c , then the value of b 4 d is equal to b ,   d ≠ 0

Correct answer

0.5

Step-by-step solution

Since the line lies on the given plane, therefore the point a , 2 d , c on the line also lies on the plane ⇒ a 2 - 2 b d + c 2 = 0 Also, the line will be perpendicular to the normal vector of the plane ⇒ a 2 - b 2 + c 2 = 0 Hence, b 2 = 2 b d ⇒ b d = 2 ⇒ b 4 d = 1 2

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