CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Anil Kumar Tondak
CBSE CLASS XII
Vector Algebra
Q. 1. Find a vector in the direction of vector 
that has magnitude 7 units.
Q. 2. Show that the points A, B and C with position vectors, 
respectively, form the vertices of a right angled triangle.
Q. 3. Find
, if two vectors 
are such that 
.
Q. 4. Find the area of the parallelogram whose adjacent sides are determined by the vectors 
Q. 5. If a unit vector 
makes angles 
with 
, 
and acute angle θ with 
, then find θ and hence the components of .
Q. 6. Let ,
and 
be three vectors such that 
and each one of them being perpendicular to the sum of other two, Find 
Q. 7. Find the value of 
Q. 8. The scalar product of the vector 
with a unit vector along the sum of vectors 
Find the value of 
.
Q. 9. If the sum of two unit vectors is a unit vector, Prove that the magnitude of their difference is 
.
Q. 10. If are position vectors of points A and B respectively, then find the position vector of points of trisection of AB.
Q. 11. Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of it.
Q. 12. ABCD is a parallelogram. If the coordinates of A, B, C are (-2, -1), (3, 0) and (1, -2) respectively, Find the co-ordinate of D.
Q. 13. Show that the points A, B, C with position vectors 
Q. 14. If a vector makes 
with OX, OY and OZ respectively, prove that 
Q. 15. If 
inclined at an angle 
, then prove that sin 
= 
.
Q. 16. If 
.
Q. 17. If 
.
Q. 18. Consider two points P and Q with position vectors
. Find the position vector of a point R which divides the line joining P and Q
in the ratio 2:1, (i) internally, and (ii) externally.
Q. 19. Find a unit vector perpendicular to each of the vectors 
Q. 20. Show that the vectors 2 i – j + k , i– 3 j – 5 k and 3 i – 4 j – 4 k form the vertices of a right angled triangle
Q. 21.
Paper By Mr. Anil Kumar Tondak
Email Id : [email protected]
