Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if ![\dfrac{x_1}{x_2}= \dfrac{y_1}{y_2}= \dfrac{z_1}{z_2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx_1%7D%7Bx_2%7D%3D%20%5Cdfrac%7By_1%7D%7By_2%7D%3D%20%5Cdfrac%7Bz_1%7D%7Bz_2%7D)
here;
![d_1 = (-1, \ 2, \ -3)](https://tex.z-dn.net/?f=d_1%20%3D%20%28-1%2C%20%5C%202%2C%20%5C%20-3%29)
Thus;
![r(t) = \dfrac{x-1}{-1} = \dfrac{y-3}{2}=\dfrac{z-0}{-3} = t](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%5Cdfrac%7Bx-1%7D%7B-1%7D%20%3D%20%5Cdfrac%7By-3%7D%7B2%7D%3D%5Cdfrac%7Bz-0%7D%7B-3%7D%20%3D%20t)
![d_2 =(2, \ -4, \ +6)](https://tex.z-dn.net/?f=d_2%20%3D%282%2C%20%5C%20-4%2C%20%5C%20%20%2B6%29)
![s(t) = \dfrac{x-0}{2} = \dfrac{y+5}{-4}=\dfrac{z-3}{6} = t](https://tex.z-dn.net/?f=s%28t%29%20%3D%20%5Cdfrac%7Bx-0%7D%7B2%7D%20%3D%20%5Cdfrac%7By%2B5%7D%7B-4%7D%3D%5Cdfrac%7Bz-3%7D%7B6%7D%20%3D%20t)
∴
![\dfrac{d_1}{d_2}= \dfrac{-1}{2} = \dfrac{2}{-4}= \dfrac{-3}{-6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd_1%7D%7Bd_2%7D%3D%20%5Cdfrac%7B-1%7D%7B2%7D%20%3D%20%5Cdfrac%7B2%7D%7B-4%7D%3D%20%5Cdfrac%7B-3%7D%7B-6%7D)
Hence, we can conclude that r(t) and s(t) are parallel.
Answer:
associative property
Step-by-step explanation:
Answer:
a 1 thousandth or 0.001
Step-by-step explanation:
This distance can be expressed as 3.84×
m.
What is distance with example?
- Distance is a scalar quantity.
- The distance of an object can be defined as the complete path travelled by an object.
Given the distance between the earth and the moon is 384000km
Representing in exponential notation,
=384000×1000m [∵1km=1000m]
=384×
m
=3.84×
m
Learn more about distance
brainly.com/question/22698433
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<u>The correct question is -</u>
The distance between the Earth and the moon is approximately 384000 km. this distance can be expressed as ____m.
Answer:
nfiuwrhiwewdjvv
Step-by-step explanation:
thats why