3D Geometry · Line intersecting two lines

Let the line

L_1

be parallel to the vector

-3\hat i + 2\hat j + 4\hat k

and pass through the point

(2, 6, 7)

and the line

L_2

be parallel to the vector

2\hat i + \hat j + 3\hat k

and pass through the point

(4, 3, 5)

. If the line

L_3

is parallel to the vector

-3\hat i + 5\hat j + 16\hat k

and intersects the lines

L_1

and

L_2

at the points

C

and

D

, respectively, then

\lvert\overrightarrow{CD}\rvert^2

is equal to:

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