O LEVEL VECTORS

Vectors

What are Vectors Addition & Subtraction of vectors Multiplication of a vector by a number Position Vectors Length of Vector Equivalence & Parallel Ratio Theorem Vectors Calculating the Modulus of a Vector In this section, you will learn how to calculate the modulus of a vector. The modulus is a mathematical term for the length or the magnitude.   The magnitude of vector x is written as |x|. The magnitude of vector   is written as |AB|.     Zero vector and unit vectors A vector with magnitude 0 is called the zero vector, written 0. A vector with magnitude 1 is called a unit vector. Vectors are equal if they have the same magnitude and the same direction. a = b  Inverse Vectors The inverse of a vector is a vector of equal magnitude but in the opposite direction. The inverse of  is - or  and the inverse of a is -a. Scalars Scalars have magnitude but not direction. Vectors can be multiplied by a scalar to produce another vector. Multiplying vector x by 3 will give a new vector 3 times the length and parallel to x. Vector addition and subtraction   When 2 vectors are added or subtracted the vector produced is called the resultant. The resultant is identified by a double arrowhead. Triangle Law: To add two vectors you apply the first vector and then the second.  + =  or a + b = c Subtracting a vector is the same as adding its inverse. a – b is the same as a + (-b) Parallelogram Law: Moving from A to C through B is the same as moving through D.  + = +  =  or a + b = b + a = c