Porisma

A hint to get started

Find a common line and use normals for the acute plane angle

For each pair of planes, find their line of intersection and acute angle. All parameters are real.

(a) r⋅(1,−1,3)=3\mathbf r\cdot(1,-1,3)=3 and r⋅(2,−1,2)=5\mathbf r\cdot(2,-1,2)=5.

(b) r=(1,2,7)+λ(1,1,0)+μ(1,0,1)\mathbf r=(1,2,7)+\lambda(1,1,0)+\mu(1,0,1) and r=(1,2,7)+s(1,2,4)+t(0,1,1)\mathbf r=(1,2,7)+s(1,2,4)+t(0,1,1).

CJC · Discussion · Question 6

Use cross products for the plane normals; a common base point simplifies the intersection line.

Read the worked solution