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## Homework Statement

Find the vector equation of the line that passes through the point Q(2,0,-5) and

is perpendicular to both the vectors m=(0,1,4) and n=(-2,-1,3).

## Homework Equations

vector equation of a line: (x, y, z)=(x

_{0},y

_{0},z

_{0}) + t(a,b,c)

cartesian equation of a line: (x-x

_{0})/a=(y-y

_{0})/b=(z-z

_{0})/c

## The Attempt at a Solution

(x

_{0},y

_{0},z

_{0})=(2,0,5)

To find (a,b,c)I know I can get two equations because the dot product of (a,b,c) with the two perpendicular lines equals zero:

b+4c=0

-2a-b+3c=0

But two equations isn't enough to solve for three variables. Also, shouldn't the point (2,0,-5) also dot product with u or v to equal zero, since it's on the same line?

Is it correct to assume that the points (0,1,4) and (-2,-1,3) are also points on the line? In which case I can easily find the direction of the line by subtracting one from the other.

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