Three Dimensional Geometry
Find the equation of the plane passing through group of points.
A(0,−1,−1),B(4,5,1) and C(3,9,4).
If a plane meets the equations axes at A,BandC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.
Find the shortest distance between lines r=(i^+2j^+k^)+λ(2i^+j^+2k^)andr=2i^−j^−k^+μ(2i^+j^+2k^)˙
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?
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
The straight line 3x−3=1y−2=0z−1 is (a)Parallel to x-axis (b)Parallel to the y-axis (c)Parallel to the z-axis (d)Perpendicular to the z-axis
The direction ratios of a normal to the plane through (1,0,0)and(0,1,0) , which makes and angle of 4π with the plane x+y=3, are a. ⟨1,2,1⟩ b. ⟨1,1,2⟩ c. ⟨1,1,2⟩ d. ⟨2,1,1⟩
If OABC is a tetrahedron where O is the origin and A, B, C are three other vertices with position vectors a⃗ , b⃗ and c⃗ respectively, then the centre of sphere circumscribing the tetrahedron is given by the position vector