Vector Algebra is fundamental for understanding geometry in 3D—especially concepts like dot product, cross product, coplanarity, orthogonality, and distances between lines/planes. These ideas frequently appear in CBSE board exams and are heavily tested in competitive exams (JEE/NEET) because they convert spatial problems into solvable algebraic computations.
25
Minutes
20
Questions
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Marking
Q1. Let and . Find the real scalar for which is minimum.
Q2. The lines and intersect for some real . The value of for which they intersect is
Q3. Let and . A vector satisfies and the volume of the parallelepiped formed by is , i.e. . Among all such , the minimum possible value of is
Q4. Find the shortest distance between the skew lines and .
Q5. Let non-zero vectors and satisfy and . The angle between and is
Q6. Let and . The scalar projection of on is
Q7. The shortest distance between the skew lines and is
Q8. For which value of are the vectors , and pairwise orthogonal?
Q9. Let and . The plane passes through the origin and contains the vectors and . The perpendicular distance from the point to the plane is
Q10. The plane passes through points , and . The foot of the perpendicular from to the plane is
Q11. If and , a unit vector perpendicular to both and with positive -component is:
Q12. Let and . For what value(s) of is coplanar with and ?
No real value of
Q13. Given , and , find a vector such that , , and the first component of is positive.
Q14. Lines and are skew. Find the points on and on such that is the shortest segment joining the lines, and compute the shortest distance .
Q15. Let non-zero vectors and be non-parallel. Consider the statements:
P: "There does not exist a vector such that
"
R: "If then is parallel to , so it cannot equal since is not parallel to ."
Which of the following is correct?
Both P and R are true and R is a correct explanation of P.
Both P and R are true but R is not a correct explanation of P.
P is true but R is false.
P is false and R is true.
...and 5 more challenging questions available in the interactive simulator.