Finding the scalar equation of a line
Formulas for the scalar equation of a line
To find the scalar equation of a line, we’ll use the formulas
???x=x_0+at???
???y=y_0+bt???
???z=z_0+ct???
where ???P_0(x_0,y_0,z_0)??? is a given point and ???v=\langle a,b,c\rangle??? is the given vector. The vector may also be in the format ???v=ai+bj+ck???.
Hi! I'm krista.
I create online courses to help you rock your math class. Read more.
How to find the scalar equation of a line from the vector function and a point in space
Take the course
Want to learn more about Calculus 3? I have a step-by-step course for that. :)
Finding the scalar equation from a point and the direction numbers
Example
Find the scalar equation of the line.
???P(2,3,1)???
???\langle2,-1,5\rangle???
Plugging the given point and the given vector into our formulas for ???x???, ???y??? and ???z???, we get
???x=2+2t???
???y=3-t???
???z=1+5t???
The scalar equation of the line is given by ???x=2+2t???, ???y=3-t??? and ???z=1+5t???.
