Question

Find the vector equation of the line through ​(0​,0​,0​) and ​(5​,1​,2​) where tequals0 corresponds to the first given point and where tequals1 corresponds to the second given point.

Answer 1

The equation of a line passing through the points (0,0,0) and (5,1,2) is:

`(x-0)/(5-0) = (y-0)/(1-0) = (z-0)/(2-0)`;

`(x)/(5) = (y)/(1) = (z)/(2)`.

Take
`(y)/(1) =t`, then
`(x)/(5)=t \\ (y)/(1)=t \\ (z)/(2)=t \\`
`\rightarrow`
`x=5t \\ y=t \\ z=2t \\`.
This is parametrical equation of a straight line, where
`y|_(t=0)=0 \\ y|_(t=1)=1`.