JEE Main20198 Apr 2019Evening ShiftMathematicsThree Dimensional GeometryActual

If a point R 4 , y , z lies on the line segment joining the points P 2 , - 3,4 and Q 8,0 , 10 , then the distance of R from the origin is

Options

A2 21
B53
C6
D2 14

Correct answer

D. 2 14

Step-by-step solution

Given point R lies on the line segment joining the points P and Q , hence direction ratios of the line P R and   P Q must be identical ⇒ 2 6 = y + 3 3 = z - 4 6 ⇒ y = - 2   and z = 6 ⇒ R 4 ,   - 2 ,   6 . Hence, distance from origin = 16 + 4 + 36 = 2 14

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