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JEE Main202127 Jul 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of the point P 3 , 4 , 4 from the point of intersection of the line joining the points Q 3 , - 4 , - 5 and R 2 , - 3 , 1 and the plane 2 x + y + z = 7 , is equal to _____.

Correct answer

0

Step-by-step solution

We have, point P 3 , 4 , 4 Equation of line joining the points Q 3 , - 4 , - 5 and R 2 , - 3 , 1 is x - 3 - 1 = y + 4 1 = z + 5 6 = r Any point on above line is - r + 3 , r - 4 , 6 r - 5 Now, satisfying it in the given plane 2 x + y + z = 7 , we get 2 - r + 3 + r - 4 + 6 r - 5 = 7 ⇒ r = 2 So, required point of intersection is T 1 , - 2 , 7 . Hence, P T = 3 - 1 2 + 4 + 2 2 + 4 - 7 2 = 7 .

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