JEE Main20211 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of line 3 y - 2 z - 1 = 0 = 3 x - z + 4 from the point ( 2 , - 1 , 6 ) is :

Options

A2 5
B2 6
C26
D4 2

Correct answer

B. 2 6

Step-by-step solution

Given equation of the line 3 y - 2 z - 1 = 0 = 3 x - z + 4 ⇒ 3 y - 1 2 = z - 0 1 = 3 x + 4 1 ⇒ x + 4 3 1 3 = y - 1 3 2 3 = z - 0 1 Here, Point on the line is P ( - 4 3 , 1 3 , 0 ) and the vector in the direction of line is 1 3 i ^ + 2 3 j ^ + k ^ then from the above diagram P R = 1 3 ( 2 + 4 3 ) + 2 3 ( - 1 - 1 3 ) + 1 ( 6 - 0 ) 1 9 + 4 9 + 1 P R = 4 14 9 Q R 2 = P Q 2 - P R 2 = 100 9 + 16 9 + 36 - 224 9 Q R = 24 = 2 6

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