# Vector equations of lines

• Aug 5th 2013, 06:38 AM
Kristen111111111111111111
Vector equations of lines
(1) Let A, B, C be the vertices of a triangle. Let a, b, c be their position vectors respectively. Find the equations of the lines through each vertex, perpendicular to the opposite side.
(2) Find the equations of the perpendicular bisectors of each side of the triangle.
• Aug 5th 2013, 07:01 AM
ebaines
Re: Vector equations of lines
Hint - if you know the slope of the line that connects points A and B then the slope of any line that is perpendicular to AB is the negative inverse of the slope of AB. Now use y = mx+b, given the x,y coordinates of point C, to determine the equation of the line that goes through C and is perpendicular to AB.
• Aug 5th 2013, 07:08 AM
Kristen111111111111111111
Re: Vector equations of lines
Thank you for your help but in this question I'm not referring to a 2-coordinate systems with only x and y axes. I'm referring to a coordinate system with x , y and z axes. I need a vector equation in the form : r = a + t(v)
• Aug 5th 2013, 07:32 AM
Plato
Re: Vector equations of lines
Quote:

Originally Posted by Kristen111111111111111111
I'm referring to a coordinate system with x , y and z axes. I need a vector equation in the form : r = a + t(v)

Suppose that $U = \overrightarrow {AB} \;,\;V = \overrightarrow {BC} \,\& \,W = \overrightarrow {AC}$

Then the line through $A$ which is perpendicular to $\overleftrightarrow {BC}$ is $\vec{a}+t(V\times(U\times W))$.

You finish the other two. Change the notation to suit yourself.
• Aug 5th 2013, 08:00 AM
Kristen111111111111111111
Re: Vector equations of lines
Thank you so much I got it :)