What is the angle between the planes2x−y+z=6 andx+y+2z=3? | Filo

Class 12

Math

3D Geometry

Three Dimensional Geometry

558
150

What is the angle between the planes2x−y+z=6 andx+y+2z=3?

1. π/2
2. π/3
3. π/4
4. π/6
Solution: [b] We know, if a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 Are two planes then angle between them is cosθ=a1a2+b1b2+c1c2a21+b21+c21−−−−−−−−−−√a22+b22+c22−−−−−−−−−−√ Let q be the angle between given planes Here, a1=2,b1=−1,c1=1;a2=1,b2=1,c2=2 ∴cosq=2×1+1×(−1)+1×24+1+1−−−−−−−√1+1+4−−−−−−−√=36=12=cosπ3 ⇒θ=π3
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