## Find if Parametric equations are perpendicular

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
stephenalistoun
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Joined: Sun Apr 10, 2011 7:31 pm
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### Find if Parametric equations are perpendicular

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

nona.m.nona
Posts: 280
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Find if Parametric equations are perpendicular

stephenalistoun wrote: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

The planes determined by the vectors corresponding to these parametric equations will intersect at an angle A of 90* (or pi/2), as will their normal vectors. So apply the formula

$\cos(A)\, =\, \frac{u \times v}{\parallel u\parallel\,\parallel v\parallel}$

Confirm the numerical result.