Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of a plane passing through the points $A(a,0,0),B(0,b,0)$ and $C(0,0,c)$.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

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 $lx−1 =my+1 =n1 and=mx+1 =ny−3 =lz−1 wherel>m>n,andl,m,n$ are the roots of the cubic equation $x_{3}+x_{2}−4x=4.$

Find the equation of plane which is at a distance $14 4 $ 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 $→ri^−j^ +2k^˙ =5and→r3i^+j^ +k^˙ =6.$

Find the angle between the lines $x−3y−4=0,4y−z+5=0andx+3y−11=0,2y=z+6=0.$