Three Dimensional Geometry
Shortest distance between the lines:r=(4i^−j^)+λ(i^+2j^−3k^) and r=(i^−j^+2k^)+u(2i^+4j^−5k^)
Show that the lines −3x+1=2y−3=1z+2 and 1x=−3y−7=2z+7 are coplanar. Find the equation of the plane containing these lines.
Show that the equation ax+by+d=0 represents a plane parallel to the z-axis. Hence, find the equation of a plane which is parallel to the z-axis and passes through the points A(2,−3,1) and B(−4,7,6).
Find the equation of the plane which contains two parallel lines given by 1x−3=−4y+2=5z and 1x−4=−4y−3=5z−2.
The direction ratios of two lines are 3,2,−6 and 1,2,2 respectively. The acute angle between these lines are