- #1
PeterSK
- 6
- 0
Homework Statement
Two planes [itex]r_1[/itex] and [itex]r_2[/itex] have the equations:
[itex]r_1 = ( 1 - \lambda ) \underline{i} + ( 2 \lambda + \mu ) \underline{j} + ( \mu - 1 ) \underline{k}[/itex]
[itex]r_2 = ( s - t ) \underline{i} + ( 2s - 3 ) \underline{j} + ( t ) \underline{k}[/itex]
If a point lies in both [itex]r_1[/itex] and [itex]r_2[/itex] then [itex]\mu =4 \lambda + 3[/itex] (shown in a previous question)
Hence find a vector equation of the line of intersection of the two planes.
Homework Equations
None known
The Attempt at a Solution
I know what I have to do but I have no idea how to do it:
- Find the normals of the planes
- Use the cross (vector) product on them to get the direction of the intersection vector
- find a point on the vector (I assume using the [itex]\mu = 4 \lambda + 3[/itex] stuff)
- substitute the two parts into the formula for a vector equation to get the answer
I'm just completely stumped!