How do you find the vector parametrization of the line of intersection of two planes 2xyz=5 and xy+3z=2?

1 Answer
Mar 22, 2015

One answer could be:

x=t

z=14t34

y=74t174.

Let's solve the system of the two equations, explaining two letters in function of the third:

2xyz=5

xy+3z=2

So:

y=2xz5

x(2xz5)+3z=2x2x+z+5+3z=2

4z=x3z=14x34

so:

y=2x(14x34)5y=2x14x+345

y=74x174.

SO:

z=14x34

y=74x174

and if we put x=t:

x=t

z=14t34

y=74t174.