Three Dimensional Geometry
If a line makes an angle of 4πwith the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is
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Find the value of λ for which the line 2x−1=3y−1=λz−1 is parallel to the plane r⋅(2i^+3j^+4k^)=4.
Find the equation of the line passing through the point P(4,6,2) and the point of intersection of line 3x−1=2y=7z+1 and the plane x+y−z=8.
Find the equation of a plane passing through the point (2,−1,5), perpendicular to the plane x+2y−3z=7 and parallel to the line 3x+5=−1y+1=1z−2.
What are the direction cosines of the y-axis?
Find the equation of the plane passing through group of points.A(2,2,−1),B(3,4,2) and C(7,0,6).
Show that the points (−3,0,1) and (1,1,1) are equidistant from the plane 3x+4y−12z+13=0.
Write the equations of line parallel to the line −3x−2=2y+3=6z+5 and passing through the point (1,−2,3).
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.