Three Dimensional Geometry
Find the equation of the plane through the line of intersection of the planes r⋅(2i^−3j^+4k^)=1 and r⋅(i^−j^)+4=0 and perpendicular to the plane r⋅(2i^−j^+k^)+8=0.
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Determine whether the following pair of lines intersect or not. (1) r=i^−5j^+λ(2i^+k^);r=2i^−j^+μ(i^+j^−k^)
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in symmetric form. Find the direction of the line.