Calculus Grade 12 University
posted by j .
8. Find the vector equation of the line in which the 2 planes 2x  5y + 3z = 12 and 3x + 4y  3z = 6 meet.

just take the crossproduct of the normals to find the direction of the vector:
 i j k 
 2 5 3 
 3 4 3 
= 3i+15j+23k
Now find a point on the line:
if x=0, y=18,z=26
the line is thus
3ti + (18+15t)j + (26+23t)k 
thanks steve.
do you know how to do these ones? :(
4. Write a vector equation of the line through the point (5, 2, 3) and parallel to the vector v=[4, 3, 1]
5. Determine an equation for the plane that is exactly between the points A(1, 2, 4) and B(3, 1, 4).
6. Find out if the line r = (1, 3, 8) + t (2, 5, 7) is parallel to the plane 3x + 4y  2z = 1
7. Where does the line r = (1, 2, 5) + t (2, 3, 1) meet the plane 2x + 5y  3z = 6? 
for the #4 i got
r = (5, 2, 3) + t(4, 3, 1)
 can you please help me on 5, 6, 7. instead since i got 4. thanks steve