JEE Main 2020 · Mathematics · Three Dimensional Geometry · hard

Let L1 pass through the origin with direction ratios (1,1,0) and L2 pass through (1,2,3) with direction ratios (0,1,1). If d is the shortest distance…

Numerical answer

Let

L_1

pass through the origin with direction ratios

(1,1,0)

and

L_2

pass through

(1,2,3)

with direction ratios

(0,1,1)

. If

d

is the shortest distance between them, find

3d^2

Show answer and solution

Answer: 4

\vec d_1\times\vec d_2=(1,-1,1)

with magnitude

\sqrt3

. Vector joining the points is

(1,2,3)

and its dot product with the cross product is

1-2+3=2

. So

d=\dfrac{2}{\sqrt3}

d^2=\dfrac43

and

3d^2=4

Original question written in the JEE Main 2020 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake