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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 l.

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 a, b,  with OX, OY and OZ  respectively, prove that sin²a+sin²b+sin²γ =2.
Q. 15. If inclined at an angle , then prove that sin = .

Q. 16. If

.
Q. 17. If

 .

Prepared By Anil Kumar Tondak
M.Sc.(Maths), M.Ed., M.A.(Eco),M.B.A.(Mkt)
Mob No. 9811363962