Question

at what points does the line: (x(t),y(t),z(t)) = (t+1,-t+1,2t+4) pass through the coordinate planes, xy plane, xz plane zy plane?

Answer 1

the original question had you find the equation of a line perpendicular to a plane with parameter t, The equation is the one i found

Answer 2

the line passes through the xy plane when z= 0
the line passes through the xz plane when y = 0
the line passes through the yz plane when x = 0

Answer 3

yeah i got for the xy plane the point (-1, -3, 0) but its wrong so I'm not sure the steps to take,

Answer 4

(x(t),y(t),z(t)) = (t+1,-t+1,2t+4)
2t + 4 = 0
t = -4/2 = -2

( -2 + 1 , -(-2) + 1 , 0) = ( -1, 3 , 0 )

Answer 5

If L is the line, L: {x=t+1 y=-t+1, x=2t+4} the point M would belong to L if the vector AM = t * the direction vector of the line

Answer 6

dammit, that right, i must have messed up a sign somewhere and missed it. thanks.