I couldn't figure out how to do the following problems.Please help.
Just give the trick and the final answer.It will do.
1.Find the equations of the line of intersection of the two planes
x-2y+3z=4
2x-3y+4z=5
2.Find the equations of the line passing through (1,1,1)and parallel to the plane 2x+3y+z+5=0
Another way to solve (1)
x-2y+3z=4
2x-3y+4z=5
are two equations in three unkowns. You can solve for two of them in terms of the third- for example, you can eliminate y by multiplying the first equation by 3, the second equation by 2 and then subtracting. Solve the resulting equation for z in terms of x. Then put that back into either equation so you have and equation in x and y only. Solve that equation for y in terms of x. Then you have x= t, y= f(t), z= g(t) as parametric equations for the line.
As for "2. Find the equations of the line passing through (1,1,1)and parallel to the plane 2x+3y+z+5=0", it makes no sense. There are an infinite number of such lines. There is an entire plane containing (1,1,1) and parallel to the given plane. Any line in that plane is a solution to this problem.