Find the distance between the skew lines with parametric equations x = 2 + t, y = 2 + 6t, z = 2t, and x = 2 + 2s, y = 4 + 14s, z = −1 + 5s.

we are given

skew lines as

L1:  x = 2 + t, y = 2 + 6t, z = 2t

L2: x = 2 + 2s, y = 4 + 14s, z = −1 + 5s

Firstly, we will find directional vector

now, we will find cross product

we are given two points as

P: (2,2,0)  and Q:(2,4,-1)

The dot product of orthogonal vectors is zero

now, we can find distance from point Q

..........Answer

y=mx+b

step-by-step explanation:

m slope, b y-intercept

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents