Determining wheter point lie on line

[salistoun]

Hi all,

How do I go about solving the following question?

Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t

Stephen

 

[DonAntonio]

Hi all,

How do I go about solving the following question?

Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t

Stephen

Just find out whether there exists a value $\,t\in\Bbb R\,$ s.t. $\,(5,-6,10)=(2+t,3-3t,4+2t)\,$ , and the same with the other vector...

DonAntonio

 

[salistoun]

Hi Don,

If I'm correct, the parametric equation for the following points is:

x = -2t + 5, y = -9t - 6 and z = -2t + 10

So no values are matching this parametric
x = 2 + t; y = 3 - 3t, z = 4 + 2t.

So therefore it does not lie on the line right?

 

[DonAntonio]

Hi Don,

If I'm correct, the parametric equation for the following points is:

x = -2t + 5, y = -9t - 6 and z = -2t + 10

So no values are matching this parametric
x = 2 + t; y = 3 - 3t, z = 4 + 2t.

So therefore it does not lie on the line right?

What is "the following point"? The point is given to you: (5,-6,10), period. You only have to solve the easy vectorial equation I wrote in my first post.

DonAntonio

 

[salistoun]

Thanks Don i do get what u saying