A vector is a quantity that has both magnitude (measurement) and direction. It’s represented by a directed line segment with an arrowhead on one end, where the length of the segment represents magnitude and the arrowhead represents direction. If an arrowhead is applied to point on , then the vector has initial point and terminal point . If vector has the same magnitude as vector , then we say . Two vectors and are if they have the same magnitude and direction regardless of the position of their initial points. if vectors and have the same magnitude but opposite directions. Note that in a typed format, when using a single letter to denote the name of a vector, we use a boldface letter, but in handwritten work, we do draw an arrow above the letter. When adding vectors together, we position each vector so that its initial point coincides with the terminal point of the preceding vector. The first vector can be placed anywhere. The sum (or resultant) is the vector that starts at the first initial point and ends at the final terminal point. Properties Commutative Property: Associative Property: If is a scalar and is a vector, the scalar multiple is defined as: If , is the vector whose magnitude is times the magnitude of and whose direction is the same as . If , is the vector whose magnitude is times the magnitude of and whose direction is opposite that of . If or if , then . Example 1 Use the given vectors to graph each of the following vectors: (a) , (b) , and (c) . – We use the symbol to represent the magnitude of a vector . Since equals the length of a directed line segment, if and only if
A vector is a quantity that has both magnitude (measurement) and direction. It’s represented by a directed line segment with an arrowhead on one end, where the length of the segment represents magnitude and the arrowhead represents direction. If an arrowhead is applied to point on , then the vector has initial point and terminal point . If vector has the same magnitude as vector , then we say . Two vectors and are if they have the same magnitude and direction regardless of the position of their initial points. if vectors and have the same magnitude but opposite directions. Note that in a typed format, when using a single letter to denote the name of a vector, we use a boldface letter, but in handwritten work, we do draw an arrow above the letter. When adding vectors together, we position each vector so that its initial point coincides with the terminal point of the preceding vector. The first vector can be placed anywhere. The sum (or resultant) is the vector that starts at the first initial point and ends at the final terminal point. Properties Commutative Property: Associative Property: If is a scalar and is a vector, the scalar multiple is defined as: If , is the vector whose magnitude is times the magnitude of and whose direction is the same as . If , is the vector whose magnitude is times the magnitude of and whose direction is opposite that of . If or if , then . Example 1 – Use the given vectors to graph each of the following vectors: (a) , (b) , and (c) . We use the symbol to represent the magnitude of a vector . Since equals the length of a directed line segment, if and only if
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