LIST OF IMPORTANT PROBLEMS AND EXPECTED QUESTIONS

FOR LEARNERS AND SLOW LEARNERS OF CLASS XII MATHEMATICS

UNIT 4: VECTOR ALGEBRA & 3D GEOMETRY:[ 17 MARKS]

01 MARK

1. Finding the values of x using definition of vectors 2. Problems using section formula3. Show that the given three vectors are collinear.4. Find the angle between the vectors5. Find the projection of a on b or b on a 6. Find the vector area of the triangle with three vertices.7. Find the area of the parallelogram whose adjacent sides are given.8. Find the area of the parallelogram whose diagonals are given.9. Finding the D.C’s and D.r’s of the given points.10. Verify the points are collinear points.11. Find the angle between two lines.12. Find the vector and the Cartesian equation of the line passing through the point and parallel

to the vector or points.13. Find the values of the constant if the lines perpendicular.14. Find the equation of the plane in normal form.15. Find the equation of the plane that passes through the three points.16. Find the constant k if the lines are orthogonal.17. Find the angle between the line and the plane.

04 MARKS:

1. Definition of vectors product , scalar product of two vectors- using problems2. Finding ratio of the position vector of the point with given position vectors.3. Finding the value of the constant with perpendicular vectors.4. Find the shortest distance between two lines.5. Find the point of contact of the two lines if they intersect.6. Find the equation of the plane passing through the point and passing through the intersection

of the planes.7. Find the equation of the plane that contains the point and is perpendicular to the planes.8. Find the distance between the two planes.9. Find the vector equation of the line passing through the point and parallel to the

planes.

06 MARKS:

1. Find the image of the point with the line or plane.2. Find the vector equation of the line passing through the point and perpendicular to the two

lines or planes.3. Find the distance of the point from the point of intersection of the line and the plane.4. Prove that problems on variable plane.