3-D geometry: Pair of Planes
We have to find the angle between the planes and value of l,m and n.
How do we approach this?
13 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.The equation of the line can be figured out by observation right? x=y=z is a trivial solution.
Angle between the planes is gonna be the tough one
So l,m,n are all 1/√3 ?
Ah I see. That works.
And angle is 90°?
Yes.
Ok, observation here is, angle between planes is angle between their normal vectors right?
And the component-wise terms of the dot product of the normal vectors are going to be the coefficients of the square terms in the product of the plane equations (P1P2=0)
Ah
So, if the normal vectors are (a1,b1,c1) and (a2,b2,c2), then the terms in the combined equation for both planes
So coeffecients of x^2, y^2 and z^2 must add to zero.
Is going to have a1a2x²+b1b2y²+c1c2z²
If they do add to zero, then the cosine of the angle is 0
If they don't, you need to solve six equations for the six components, and then dot product
Ahh I see.
Nice solution.
+solved @Opt
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