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.
Asked by: USER7952
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182 Answers
Answer (182)
The equation of a line passing through the points (0,0,0) and (5,1,2) is:
[tex] \frac{x-0}{5-0} = \frac{y-0}{1-0} = \frac{z-0}{2-0} [/tex];
[tex] \frac{x}{5} = \frac{y}{1} = \frac{z}{2} [/tex].
Take [tex] \frac{y}{1} =t[/tex], then [tex] \frac{x}{5}=t \\ \frac{y}{1}=t \\ \frac{z}{2}=t \\ [/tex] [tex]\rightarrow [/tex] [tex]x=5t \\ y=t \\ z=2t \\ [/tex].
This is parametrical equation of a straight line, where [tex]y|_{t=0}=0 \\ y|_{t=1}=1[/tex].
[tex] \frac{x-0}{5-0} = \frac{y-0}{1-0} = \frac{z-0}{2-0} [/tex];
[tex] \frac{x}{5} = \frac{y}{1} = \frac{z}{2} [/tex].
Take [tex] \frac{y}{1} =t[/tex], then [tex] \frac{x}{5}=t \\ \frac{y}{1}=t \\ \frac{z}{2}=t \\ [/tex] [tex]\rightarrow [/tex] [tex]x=5t \\ y=t \\ z=2t \\ [/tex].
This is parametrical equation of a straight line, where [tex]y|_{t=0}=0 \\ y|_{t=1}=1[/tex].