Three Dimensional Geometry
Find the vector equation of the plane through the point (3i^+4j^−k^) and parallel to the plane r⋅(2i^−3j^+5k^)+5=0.
Perpendiculars are drawn from points on the line 2x+2=−1y+1=3z to the plane x+y+z=3 The feet of perpendiculars lie on the line (a) 5x=8y−1=−13z−2 (b) 2x=3y−1=−5z−2 (c) 4x=3y−1=−7z−2 (d) 2x=−7y−1=5z−2
A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),andC(−1,1,2), then angle between face OABandABC will be a. cos−1(3117) b. 300 c. 900 d. cos−1(3519)
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
If the lines −3x−1=2ky−2=−2z−3and3kx−1=1y−5=−5z−6 are at right angle, then find the value of k˙
The projection of the line −1x+1=2y=3z−1 on the plane x−2y+z=6 is the line of intersection of this plane with the plane a. 2x+y+2=0 b. 3x+y−z=2 c. 2x−3y+8z=3 d. none of these
Find the point where line which passes through point (1,2,3) and is parallel to line r=i^+j^+2k^+λ(i^−2j^+3k^) meets the xy-plane.
Find the equation of a plane which is parallel to the plane x−2y+2z=5 and whose distance from thepoint (1,2,3) is 1.