Hello. Could somebody please help me out on some questions about intersecting planes? This is rather urgent so if you could help me out quickly, it'll be great.
Two vectors a and b are the normals to two planes. Both of these planes pass through (0,0,0). Vector OP = t[a x b] where t is a scalar.
1. Describe the set of all points P in relation to the two distinct planes
For this one, can somebody perhaps explain it in "simpler" terms because I'm rather confused on the wording of it.
2. From above or otherwise, find the parametric equations of the line of intersection between the two planes
5x + 2y - z = 0
3x + y + 4z = 0
Okay, first, I got the direction vectors of the two equations which are [5,2,-1] and [3,1,4].
From there, I cross-producted these two vectors to get [7,-17,-1] which is the perpendicular of the two vectors. Now vector OP is [7t,-17t,-t] where t is a scalar. Therefore P is (7t,-17t,-t). Also, (7,-17,-1) lies on both planes and hence, lies on the line of intersection.
So I have two points (0,0,0) and (7,-17,-1) which lie on the line of intersection.
Is what I did above correct? If so, what would be the next step to take?
3. Show the line of intersection from before is parallel to plane 4x + y + 11= 26
I'll need to do the above question first to answer this one so once I get an answer for it, I'll attempt to do this one.
Thankyou, all help is appreciated.