Three Dimensional Geometry
The image of the line 3x−1=1y−3=−5z−4in the plane 2x−y+z+3=0is the line
Find the vector equation of line passing through the point (1,2,−4) and perpendicular to the two lines: 3x−8=−16y+19=7z−10and3x−15=8y−29=−5z−5
Find the equation the plane which contain the line of intersection of the planesri^+2j^+3k^˙−4=0andr2i^+j^−k^˙+5=0 and which is perpendicular to the plane r(5i^+3j^−6k^)+8=0 .
A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?
A mirror and source of light are situated at the origin O and a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1,−1,1, then DCs for the reflacted ray are :
Find the shortest distance between lines r=(i^+2j^+k^)+λ(2i^+j^+2k^)andr=2i^−j^−k^+μ(2i^+j^+2k^)˙