Three Dimensional Geometry
Find the vector equation of the plane passing through the point (1,1,1) and parallel to the plane r⋅(2i^−j^+2k^)=5.
A plane passes through a fixed point (a, b, c). The locus of the foot of the perpendicular to it from the origin is the sphere
L1 and L2 are two lines whose vector equations are L1:r⃗ =λ((cosθ+3√)i^+(2√sinθ)j^+(cosθ−3√)k^)L2:r⃗ =μ(ai^+bj^+ck^), where λ and μ are scalars and α is the acute angle between L1 andL2. If the angle ′α′ is independent of θ then the value of ′α′ is
The Cartesian equations of a line are 6x−2=3y+1=2z−2. Find its direction ratios and also find a vector equation of the line.