Three Dimensional Geometry
The angle between the lines whose direction cosines satisfy the equations l+m+n=0and l2=m2+n2is
A mirror and a source of light are situated at the origin 0 and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction consines of the reflected rays are
Find the locus of appoint which moves such that the sum of the squares of its distance from the points A(1,2,3),B(2,−3,5)andC(0,7,4)is120.
Find the value of m for which thestraight line 3x−2y+z+3=0=4x+3y+4z+1 is parallel to the plane 2x−y+mz−2=0.
Find Cartesian and vector equation of the line which passes through the point (−2,4,−5) and parallel to the line given by 3x+3=5y−4=6z+8 .
The lines which intersect the skew lines y=mx,z=c;y=−mx,z=−c and the x-axis lie on the surface: (a.) cz=mxy (b.) xy=cmz (c.) cy=mxz (d.) none of these
Find the equation of the sphere described on the joint of points AandB having position vectors 2i^+6j^−7k^and−2i^+4j^−3k^, respectively, as the diameter. Find the center and the radius of the sphere.
Let A(a⃗ ) and B(b⃗ ) be points on two skew line r⃗ =a⃗ +λ⃗ and r⃗ =b⃗ +uq⃗ and the shortest distance between the skew line is 1, where p⃗ and q⃗ are unit vectors forming adjacent sides of a parallelogram enclosing an area of 12units. If an angle between AB and the line of shortest distance is 60∘, then AB=