Three Dimensional Geometry
Show that the points A(2,3,4),B(−1,−2,1) and C(5,8,7) are collinear.
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Find the equation of the plane passing through the point (1,−2,7) and parallel to the plane 5x+4y−11z=6.
The Cartesian equation of a line are 2x−2=3y+1=−2z−3. What is its vector equation?
Show that the line x=(2i^−2j^+3k^)+λ(i^−j^+4k^) is parallel to the plane r⋅(i^+5j^+k^)=7.
Find the angle between the lines r=(2i^−5j^+k^ )+λ(3i^+2j^+6k^ ) and r=(7i^−6k^ )+μ(i^+2j^+2k^ )
Prove that the lines 1x−2=4y−4=7z−6 and 3x+1=5y+3=7z+5 are coplanar. Also find the equation of the plane containing these lines.
Find the angle between the line r=(i^+2j^−k^)+λ(i^−j^+k^) and the plane r⋅(2i^−j^+k^)=4.
Write the angle between the line 2x−1=1y−2=−2z+3 and the plane x+y+4=0.
What are the direction cosines of the y-axis?