Three Dimensional Geometry
Find the equation of a plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c).
The angle between the straight lines r⃗ =(2−3t)i⃗ +(1+2t)j⃗ +(2+6t)k⃗ and r⃗ =(1+4s)i⃗ +(2−s)j⃗ +(8s−1)k⃗ is
Find the equation of the sphere which passes through (10,0),(0,1,0)and(0,0,1) and whose centre lies on the plane 3x−y+z=2.
Find the acute angle between the lines lx−1=my+1=n1and=mx+1=ny−3=lz−1wherel>m>n,andl,m,n are the roots of the cubic equation x3+x2−4x=4.
Find the equation of plane which is at a distance 144 from the origin and is normal to vector 2i^+j^−3k^˙
The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.
Value ofλ such that the linex−12=y−13=z−1λIs perpendicular to normal to the planer⃗ .(2i⃗ +3j⃗ +4k⃗ )=0 is
Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes →ri^−j^+2k^˙=5 and →r3i^+j^+k^˙=6.