Three Dimensional Geometry
Find the value of λ for which the given planes are perpendicular to each other.
r⋅(2i^−j^−λk^)=7 and r⋅(3i^+2j^+2k^)=9.
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⟩
Find the equation of the plane which is parallel to the lines r=i^+j^+λ(2i^+j^+4k^)and−3x+1=2y−3=1z+2 and is passing through the point (0,1,−1 ).
Find the equation of the sphere described on the joint of points AandB having position vectors 2i^+6j^−7k^and−2i^+4j^−3k^, respectively, as the diameter. Find the center and the radius of the sphere.
Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axesI.cos2α+cos2β+cos2γ=−1II. sin2α+sin2β+sin2γ=1Whichoftheaboveiasrecorrect?