Three Dimensional Geometry
Show that the points (−3,0,1) and (1,1,1) are equidistant from the plane 3x+4y−12z+13=0.
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 :
If a line makes angles α,βandγ with threew-dimensional coordinate axes, respectively, then find the value of cos2α+cos2β+cos2γ˙
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 vector equation of the following planes in Cartesian form: r=i^−j^+λ(i^+j^+k^)+μ(i^−2j^+3k^)˙
A line makes 45∘ with positive x-axis and makes equal angles with positive y, z axes, respectively. What is the sum of the three angles which the line makes with positive x, y and z axes?