Determine the parametric equations of the line given the following: determine the parametric equations of the line whose direction vector is perpendicular to the direction vectors of the two lines `(x)/(-4)`=`(y+10)/-7`=`(z+2)/3` and `(x-5)/3`=`(y-5)/2`=`(z+5)/4` and passes through the point (2,-5,0)

Expert Answers

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Because the line you are looking for is perpendicular to the other two lines, its direction vector is a multiple of the cross product of the direction vectors of the other two lines.

The direction vector of the first line is [-4, -7, 3] and the direction vector of the second line is [3, 2, 4] so the cross product is [-34, 25, 13].  We can use any multiple of this for the direction vector, so let's just use a multiple of 1 (that is, we'll use [-34, 25, 13])

Now use the point given to get the parametric equations:




where t is the parameter, and 2, -5 and 0 came from the point that the line passes through.

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