Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
The parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Also, the point (17,–30,31) does not lie on the line.
for given question,
We need to find the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1)
Let [tex]\vec r_0= < 5,2,7 >[/tex]
and
[tex]\vec v= < 8-5,-6-2,1-7 > \\\\\vec v= < 3,-8,-6 >[/tex]
where vector v is the direction vector.
So, the equation of the line would be,
[tex]\vec r=\vec r_0+\lambda \vec v\\\\\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Now we need to determine whether the point (17, -30, 31) is on the line.
Let [tex]< 17,-30,31 > = < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
For first component,
⇒ 17 = 5 + 3λ
⇒ 3λ = 12
⇒ λ = 4
For the second component,
⇒ -30 = 2 - 8λ
⇒ -8λ = -32
⇒ λ = 4
For third component,
⇒ 31 = 7 - 6λ
⇒ -6λ = 24
⇒ λ = -4
since the values of the λ are not consistent, the point (17,–30,31) does not lie on the line.
Therefore, the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]
Also, the point (17,–30,31) does not lie on the line.
Learn more about the parametric equation of the line here:
https://brainly.com/question/9056657
#SPJ4
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
