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Firstly you are finding the intersect of 2 planes, that will only ever give you a line at best.

([br]974010340[br])\left(\begin{array}{ccc|c} [br]9 & 7 & 4 & 0 \\ -10 & 3 & 4 & 0[br]\end{array}\right)

Convert to RREF

([br]10169700176970[br])\left(\begin{array}{ccc|c} [br]1 & 0 & -\frac{16}{97} & 0 \\ 0 & 1 & \frac{76}{97} & 0[br]\end{array}\right)

a1697c=0a - \frac{16}{97}c = 0
b7697c=0b - \frac{76}{97}c = 0

a=1697ca = \frac{16}{97}c
b=7697cb = -\frac{76}{97}c


The fact that they both equal zero makes it a lot easier, since we can just take 0,0,0 as the fist point.

Since c is the free variable, let c = 97
a = 16, b = -76

So the solution is the line:
Unparseable latex formula:

\left(\begin{array}{n} a \\ b \\ c \end{array}\right) = t \left(\begin{array}{c} 16 \\ -76 \\ 97 \end{array}\right)





Edit, you could pick any value for c, it doesn't matter since you are multiplying by the variable t. I only picked 97 to remove the fractions and make it look nicer.
(edited 13 years ago)

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