Three Dimensional Geometry
If the cartesian equations of a line are 53−x=7y+4=42z−6, write the vector equation for the line
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Show that the lines α−δx−a+d=αy−a=α+δz−a−d
Find the angle between any two diagonals of a cube.
Find the equation of a plane which passes through the point (1,2,3)
and which is equally inclined to the planes x−2y+2z−3=0and8x−4y+z−7=0.
A parallelepiped is formed by planes drawn through the points P(6,8,10)and(3,4,8)
parallel to the coordinate planes. Find the length of edges and diagonal of the parallelepiped.
Find the shortest distance between the lines r=(1−λ)i^+(λ−2)j^+(3−2λ)k^andr=(μ+1)i^+(2μ+1)k^˙
Find the equation of the plane through the points (23,1)and(4,−5,3)
and parallel to the x-axis.
Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' respectively from the origin, then1a2+1b2+1c2=k(1a′2+1b′2+1c′2), where k is equal to
The angle between the pair of planes represented by equation2x2−2y2+4z2+6xz+2yz+3xy=0is