## IBDP Mathematics Applications & Interpretations HL Chapter 7 Notes

vectors

STUDY NOTES FOR MATHEMATICS – CHAPTER 7 – VECTORS

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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

Scalar quantities only have magnitude while vector quantities have both magnitude and direction. Vector quantities can be represented using directed line segments or arrows. The length of the arrow represents the size or magnitude of the quantity and the head of the arrow shows its direction. The position vector of point A is the vector from the origin to point A. Two vectors are equal if they have the same magnitude and direction. The negative of a vector a is the vector parallel to a and with the same length but in the opposite direction. To construct a + b, first, draw a and then draw b at the arrowhead end of a. Then, join the beginning of a to the arrowhead end of b. To subtract one vector from another, we add its negative: a – b = a + (-b). When it comes to plotting points in the Cartesian plane, we move first in the x-direction and then in the y-direction. A translation vector is used to translate a point a units in the x-direction and b units in the y-direction. The magnitude of a vector can be found using the Pythagoras theorem.

The equation of a line using its direction and any fixed point on the line can be determined in both 2-dimensional and 3-dimensional geometry. The vector equation of a line is r = a + 𝜆b. To find the acute angle between two lines, we use the formula , where b1 and b2 are the direction vectors of the given lines. The position of an object moving with a constant velocity can be modelled using vectors, where the velocity vector of the motion gives the direction vector of the line, time is the parameter and the initial position of the object gives a fixed point on the line. The shortest distance from a point of a line will also be discussed in this chapter. This includes finding the foot of the perpendicular and calculating the shortest distance using for problems in 3 dimensions. To find the shortest distance between two objects with constant velocity, the quadratic theory can be applied. The vector equations of intersecting lines in 2 dimensions can be solved simultaneously to find the point where the lines intersect. 