Three Dimensional Geometry
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.
If P(x,y,z) is a point on the line segment joining Q(2,2,4)andR(3,5,6) such that the projections of OP on the axes are 13/5, 19/5 and 26/5, respectively, then find the ratio in which P divides QR˙
Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' respectively from the origin, then1a2+1b2+1c2=k(1a′2+1b′2+1c′2), where k is equal to
If r⃗ =(i^+2j^+3k^)+λ(i^+j^+k^) and r⃗ =(i^+2j^+3k^)+μ(i^+j^−k^) are two lines, then the equation of acute angle bisector of two lines is
Find the direction ratios of orthogonal projection of line 1x−1=−2y+1=3z−2 in the plane x−y+2z−3=0. also find the direction ratios of the image of the line in the plane.
Find the angel between the following pair of lines: r=2i^−5j^+k^+λ(3i^+2j^+6k^)andr=7i^−6k^+μ(i^+2j^+2k^) 2x=2y=1zand4x−5=1y−2=8z−3