If a point R(4, y, z) lies on the line segment joining the… — JEE Main 2019 Mathematics PYQ

JEE Main 2019 · 8 April · Shift II

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

A.
$2\sqrt{21}$
B.
$\sqrt{53}$
C.
$2\sqrt{14}$
D.
$6$

Show answer and solution

Correct option: C

Solution

The direction ratios of PQ are (6, 3, 6), so parametrically a point on PQ is (2+6t, -3+3t, 4+6t). Setting x = 4 gives 2+6t = 4, so t = 1/3. Then y = -3 + 3(1/3) = -2 and z = 4 + 6(1/3) = 6. So R = (4, -2, 6), and its distance from the origin is √(16 + 4 + 36) = √56 = 2√14.

[JEE Main 2019 · 8 April · Shift II]

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JEE Main 2019 Mathematics question on Three Dimensional Geometry