Vector Algebra forms the foundation for understanding 3D geometry in Class 12 and is heavily used in board and competitive exams. Mastery of dot product, cross product, scalar triple product, and vector equations helps solve problems on angles between vectors, projections, coplanarity, shortest distances between lines, and plane geometry efficiently and accurately.
25
Minutes
20
Questions
1 / -0
Marking
Q1. If and , the scalar component of along is:
Q2. If non-zero vectors satisfy and , then the angle between and is:
Q3. Let and . The coordinates of the point on the line closest to the origin are:
Q4. If non-zero vectors satisfy , then the value of is:
Q5. Does there exist a vector such that and ?
Yes, exactly one such vector exists.
No such vector exists.
Yes, infinitely many such vectors exist.
Yes, but the number of such vectors is finite and greater than one.
Q6. Let be unit vectors with . The magnitude of is
Q7. Let be the line through with direction vector and let be a point. The shortest distance from to equals
Q8. For which values of are the vectors , and coplanar?
Q9. Let be unit vectors in satisfying . The value of is
Q10. The lines and intersect for which value of ?
Q11. Given vectors and with and , find .
Q12. Find the value of for which the lines
are perpendicular and intersect.
Q13. Let satisfy . If is a unit vector perpendicular to , what is the maximum possible value of ?
Q14. The shortest distance between the skew lines
is
Q15. Let be non-zero vectors in . If is parallel to , then which of the following must be true?
is parallel to .
are coplanar.
.
are collinear.
...and 5 more challenging questions available in the interactive simulator.