Three Dimensional Geometry
Find the value of m for which the line r=(i^+2k^)+λ(2i^−mj^−3k^) is parallel to the plane r⋅(mi^+3j^+k^)=4.
Find the equation of the plane which passes through the point (1,2,3) and which is at the minimum distance from the point (−1,0,2)˙
A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?
The vector equation of the line of intersection of the planes r⃗ =b⃗ +λ1(b⃗ −a⃗ )+μ1(a⃗ −c⃗ ) and r⃗ =b⃗ +λ2(b⃗ −c⃗ )+μ2(a⃗ +c⃗ )a⃗ ,b⃗ ,c⃗ being non-coplanar vectors, is
ABC is a triangle and A=(2,3,5),B=(-1,3,2) and C= (λ,5,μ). If the median through A is equally inclined to the axes, then find the value of λ and μ