CBSE CLASS XII
Three Dimensional Geometry
Q. 1. Find the direction cosines of X, Y and Z-axis.
Q. 2. Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector .
Q. 3. Find the value of p so that the lines
Q. 6. Find the vector equation of the plane passing through the intersection of planes
Q. 8. Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then
Q. 10. Find the equation of the line passing through the point (-1, 3, -2) and perpendicular to the lines
Q. 11. Find the foot of the perpendicular drawn from the point (0, 2, 3) on the line Also, find the length of the perpendicular.
Q. 12. Find the shortest distance between the following pairs of lines whose cartesian equations are :
Q. 13. A plane meets the coordinate axis in A, B, C such that the centroid of triangle ABC is the point (p,q,r). Show that the equation of the plane is .
Q. 14. Find the equation of the plane passing through the point (1, 1, -1) and perpendicular to the planes x + 2y + 3z – 7=0 and 2x – 3y + 4z = 0.
Q. 15. Find the distance between parallel planes,
Q. 16. Show that the lines :
Prepared By Anil Kumar Tondak