NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The distance of the point 1 , 2 , 3 from the plane x + y - z = 5 measured along the straight line x = y = z is

Options

A5 3 units
B10 3 units
C3 3 units
D3 5 units

Correct answer

A. 5 3 units

Step-by-step solution

Equation of line parallel to the line x = y = z and passing through (1, 2, 3) is x - 1 = y - 2 = z - 3 Coordinates of a general point on this line is λ + 1 , λ + 2 , λ + 3 . It meets the given plane x + y - z = 5 ⇒ λ = 5 So, the point of intersection is 6 , 7 , 8 Hence, distance = 5 3

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