Question

The line $l_1$ passes through the point $(2,6,2)$ and is perpendicular to the plane $2 x+y-2 z=10$. Then the shortest distance between the line $l_1$ and the line $\frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2}$ is :

• A. $\frac{19}{3}$
• B. 7
• C. 9
• D. $\frac{13}{3}$

Answer 1

Answer: (C)

9

Answer 2

Line ℓ, is given by
L1​:2x−2​=1y−6​=−2z−2​
Given,
L2​:2x+1​=−3y+4​=2z​

Shortest distance =∣∣​MNAB⋅MN​∣∣​
AB=3i^+10j^​+2k^
MN=∣∣​i^22​j^​1−3​k^−22​∣∣​=−4i^−8j^​−8k^
MN=16+64+64​=12
∴ Shortest distance =∣∣​12−12−80−16​∣∣​=9
∴