Vectors

Maths, HSSC-KPK First Year. This chapter is split into 56 topics and has 1,453 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Scalar multiples on a grid and special quadrilaterals 26 questions
2. Addition and subtraction of plane vectors 26 questions
3. Equal vectors and finding unknowns in the plane 26 questions
4. Midpoint theorem and diagonals of a parallelogram 26 questions
5. Rectangular coordinate system in space 27 questions
6. Area of a triangle using the cross product 26 questions
7. Moment of a force about a point 27 questions
8. Angle between two vectors using the cross product 26 questions
9. Volume of a parallelepiped 27 questions
10. Properties of the magnitude of a vector 27 questions
11. Geometrical representation of a vector 23 questions
12. Unit vector in the direction of a plane vector 27 questions
13. Vector joining two points in the plane 26 questions
14. Area of a parallelogram using the cross product 26 questions
15. Ratio formula and position vector of a dividing point 27 questions
16. Anticommutative and distributive properties of the cross product 26 questions
17. Geometrical results proved with the dot product 27 questions
18. Vector methods for points and parallelograms in the plane 26 questions
19. Cross products of the unit vectors i j and k 27 questions
20. Volume of a tetrahedron 26 questions
21. Scalars and vectors 22 questions
22. Direction numbers (ratios) and vectors from direction cosines 26 questions
23. Vector relations in triangles and parallelograms 26 questions
24. Magnitude equal and negative vectors 22 questions
25. Distance between two points in space 27 questions
26. Properties of the scalar triple product 26 questions
27. Dot (scalar) product definition 26 questions
28. Review exercise 3 selected problems 26 questions
29. Algebraic properties of vectors 26 questions
30. Magnitude and unit vector of a vector in space 27 questions
31. Centroid of a triangle and length of a median 26 questions
32. Dot product in terms of components 26 questions
33. Work done by a constant force 27 questions
34. Projection of one vector on another 26 questions
35. Magnitude of a plane vector 27 questions
36. Orthogonal vectors and perpendicularity conditions 27 questions
37. Algebra of vectors in space 27 questions
38. Scalar triple product definition and determinant form 26 questions
39. Direction angles and direction cosines 26 questions
40. Subtraction and scalar multiplication of vectors 26 questions
41. Angle between two vectors using the dot product 27 questions
42. Cross (vector) product definition and right-hand rule 26 questions
43. Linear combinations of plane vectors 26 questions
44. Properties of the dot product 26 questions
45. Cross product in terms of components 26 questions
46. Zero unit and parallel vectors 24 questions
47. Consequences of the definition of the cross product 26 questions
48. Vectors in a regular hexagon 24 questions
49. Dot product of parallel and orthogonal vectors and of i j k 26 questions
50. Section formula for a point dividing a segment in space 26 questions
51. Position vector 23 questions
52. Coplanar vectors and coplanar points 26 questions
53. Triangle parallelogram and polygon laws 26 questions
54. Representation of vectors in the Cartesian plane 26 questions
55. Vectors in space and the unit vectors i j k 26 questions
56. Unit and sized vectors perpendicular to two vectors 26 questions