University:
Virtual High School
Course:
MCV4U | Calculus and Vectors
Academic year:

2023
Views:

29

Pages:

2
Author:

anon

MCV4U – Grade 12 Calculus & Vectors – Geometric Vectors Test Vectors ● Vector: is a quantity that has direction and magnitude ● Scalar: is a quantity that only has magnitude ● True Bearing: is directed compass measurement, beginning at North and rotating clockwise. ● Quadrant Bearing: is a compass measurement east or west of the NorthSouth line ● Equivalent Vectors: are equal in magnitude and direction. ○ Vectors can be translated anywhere on the same plane and still be equivalent ● Oppose Vectors: are equal in magnitude, but opposite in direction ● Vectors can be Adding and Subtracting Vectors ● Vectors can be moved around to create diagrams that are easier to solve because they remain equivalent regardless of where they are translated. ● Adding Vectors using Tail to head method using a triangle or tail to tail method using a parallelogram. ● The resultant is a vector joining the head of the first vector to the tail of the last vector ● If 2 vectors, a and b, are parallel in the same direction, |a + b| = |a| + |b| and in the same direction ● If a and b have opposite directions and | a | > | b |, then | a + b | = | a | – | b | and a + b is in the same direction as a. ● Subtract vectors by adding the opposite vector ● Zero Vector: means there is no magnitude or direction. Addition of 2 opposite vectors ● Vectors follow commutative, associative, and identity properties ○ They can be added in any order ○ Simplifying vector expressions is similar to simplifying integer expressions Scalar Vector Multiplication ● When a vector is multiplied by a scalar, the vectors are parallel and the scalar multiplies the magnitude of the vector. If the scalar is positive, the direction doesn't change; if it's negative, it becomes the opposite. ● Multiplying vectors follow the distributive and associative rule ○ They can be expanded using FOIL ○ They can be multiplied in any order ● Linear Combination of vectors can be formed by adding scalar multiples of 2 or more vectors. Applications of Geometric Vectors ● 2 Vectors that are perpendicular to each other and add together to give a vector v are called the rectangular vector components of v. ● When solving resultants, you can use Vector operations, pythagorean theorem, or trigonometry. ● Equilibrant Vector: is the opposite of the resultant

MCV4U - Geometric Vectors Test

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