# Find if Parametric equations are perpendicular

1. May 12, 2012

### salistoun

Hi all,

How do you find out if this Parametric equation

x = -2t + 3 ; y = -t - 1 ; z = -3t + 2

Is perpendicular to this parametric equation

x = -2 + 6t ; y = 3 - 6t ; z = -3 - 2t

Thanks
Stephen

2. May 13, 2012

### haruspex

The constant terms won't affect it, will they? I.e., can't you replace each line by one parallel to it through the origin, and do that simply by omitting the constant terms?
Then it will be just a matter of checking that the dot product of the two 3-d vectors is zero.

3. May 13, 2012

### chiro

Hey salistoun.

Do you know how to get the direction vector for both parametric representations? How can you test whether two vectors are orthogonal with the dot product?

4. May 13, 2012

### HallsofIvy

Staff Emeritus
I was sorely tempted to say that equations, whether parametric or not, are never perpendicular- "perpendicular" is only defined for geometric objects.

But you mean "are the lines given by these parametric equations perpendicular".

The line given by parametric equations $x= A_1t+ B_1$, $y= C_1t+ D_1$, $z= E_1t+ F_1$ and $x= A_2t+ B_2$, $y= C_2t+ D_2$, $z= E_2t+ F_2$ are perpendicular if amd only if their direction vectors $<A_1, C_1, F_1>$ and $<A_2. C_2, F_2>$ are perpendicular which, again, is true if and only if their dot product, $<A_1, C_1, F_1>\cdot<A_2, C_2, F_2>= A_1A_2+ C_1C_2+ F_1F_2= 0$.