Three Dimensional Geometry
Find the vector and Cartesian forms of the equations of the plane containing the two lines r=(i^+2j^−4k^)+λ(2i^+3j^+6k^) and r=(3i^+3j^−5k^)+μ(−2i^+3j^+8k^).
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Distance of the point P(p) from the line r=a+λb is a. ∣∣(a−p)+∣∣b∣∣2((p−a)b˙)b∣∣ b. ∣∣(b−p)+∣∣b∣∣2((p−a)b˙)b∣∣ c. ∣∣(a−p)+∣∣b∣∣2((p−b)b˙)b∣∣ d. none of these
Find the unit vector perpendicular to the plane r2i^+j^+2k^˙=5.
Find the angel between the lines 2x=3y=−zand6x=−y=−4z˙
The distance of point A (-2, 3, 1) from the line PQ through P (- 3, 5, 2), which makes equal angles with the axes is
Find the angel between the planes 2x+y−2x+3=0andr6i^+3j^+2k^˙=5.
The equation of the plane which makes with co-ordinate axes, a triangle with its centroid (α,β,γ)is
Fid the condition if lines x=ay+b,z=cy+dandx=aprimey+bprime,z=cprimey+d′
The point of intersecting of the line passing through (0,0,1) and intersecting the lines x+2y+z=1,−x+y−2z=2andx+y=2,x+z=2 with xy-plane is