posted by jack
Hi, I was working on my math homework and I was stumbling on these problems. I tried looking at the solutions but my answers were completely off. Here are the ones I'm stuck on:
If vectors O(0,0,0), A(6,0,0), B(6,-sqrt(24), sqrt(12)), and C(0,-sqrt(24), sqrt(12)) form a square.
1) Show that an equation of the plane II, containing the square OABC, is y + sqrt(2)z = 0.
2) Find a vector equation of the line L, through M (the midpoint of OB), perpendicular to the plane II.
3) Find the coordinates of D, the point of intersection of the line L with the plane whose equation is y = 0.
4) Find the coordinates of E, the reflection of the point D in the plane II.
5) Find the angle of ODA, and what this tells you about the solid OABCDE.
The other question is:
Consider the points A(1,0,0), B(2,2,2), and C(0,2,1).
1) Show that the Cartesian equation of the plane II(1) containing the triangle ABC is 2x+3y-4z=2.
2) A second plane II(2) is defined by the Cartesian equation II(2): 4x-y-z=4. Find the vector equation of L1: the intersection of the planes II(1) and II(2).
3) A third plane II(3) is defined by the Cartesian equation 16x + ay - 3z = b. Find the value of a if all three planes contain L1.
4) Find conditions on a and b if the plane II(3) does not intersect with L1.
Thank you so much for your help in advance. I really appreciate it.