NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A plane P passes through the point 1,1 , 1 and is parallel to the vectors a → = - i ^ + j ^ and b → = i ^ - k ^ . The distance of the point 3 3 2 , 3 3 , 3 from the plane is equal to

Options

A3 units
B9 2 units
C3 3 units
D3 units

Correct answer

B. 9 2 units

Step-by-step solution

Equation of the plane is x - 1 y - 1 z - 1 - 1 1 0 1 0 - 1 = 0 ⇒ x - 1 - 1 - y - 1 1 + z - 1 - 1 = 0 ⇒ x + y + z - 3 = 0 The distance of point 3 3 2 , 3 3 , 3 from x + y + z - 3 = 0 is 3 3 2 + 3 3 + 3 - 3 3 = 9 2 units

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