Three Dimensional Geometry
The length of the projection of the line segment joining the points (5,−1,4) and (4,−1,3) on the plane x+y+z=7 is
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Find the Cartesian and vector equations of a plane passing through the point (1,2,−4) and parallel to the lines 2x−1=3y−2=6z+1 and 1x−1=1y+3=−1z.
Find the vector equation of a plane whose Cartesian equation is 5x−7y+2z+4=0.
Find the equation of a plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c).
Show that the following pairs of planes are at right angles.x−2y+4z=10 and 18x+17y+4z=49.
Find the equation of the plane passing through the point (1,4,−2) and parallel to the plane 2x−y+3z+7=0.
Find the acute angle between the following planes.2x−y+z=5 and x+y+2z=7.
Find the equation of the plane passing through the points A(−1,1,1) and B(1,−1,1) and perpendicular to the plane x+2y+2z=5.
Reduce the equation of the plane 4x−3y+2z to the intercept form, and hence find the intercepts made by the plane with the coordinate axes.