Three Dimensional Geometry
Find the angle between the line r=(i^+2j^−k^)+λ(i^−j^+k^) and the plane r⋅(2i^−j^+k^)=4.
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 equation of the plane passing through A(2,2,−1),B(3,4, 2)andC(7,0,6)˙ Also find a unit vector perpendicular to this plane.
If OABC is a tetrahedron where O is the origin and A, B, C are three other vertices with position vectors a⃗ , b⃗ and c⃗ respectively, then the centre of sphere circumscribing the tetrahedron is given by the position vector
The line which passes through the origin and intersect the two lines x−12=y+34=z−53,x−42=y+33=z−144, 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.