Three Dimensional Geometry
Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0and2lm+2nl−mn=0.
The d. r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x+y=3 are
The Cartesian equations of a line are 6x−2=3y+1=2z−2. Find its direction ratios and also find a vector equation of the line.
A plane passes through a fixed point (a,b,c)˙ Show that the locus of the foot of the perpendicular to it from the origin is the sphere x2+y2+z2−ax−by−cz=0.
A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following1.sin2θ+sin2ϕ=cos2ψ2. cos2θ+cos2ϕ=sin2ψ3.sin2θ+cos2ϕ=cos2ψWhich of the above is/are correct?
The plane x+3y+13=0 passes through the line of intersection of the planes 2x−8y+4z=pand3x−5y+4z+10=0. If the plane is perpendicular to the plane3x−y−2z−4=0, then the value of p is equal to