Vectors A vector is a quantity that has

Vectors A vector is a quantity that has both magnitude an direction

Geometric Vectors §

Finding Vector Magnitude

Find the magnitude

Find the magnitude

Representing Vectors in Rectangular Coordinates §

Operations with Vectors §

More operations. §

Homework: p. 709 1 -4, 13 -37 odds.

Adding Vectors § v = w if v and w have the same direction and magnitude § The sum v + w of two vectors is defined as the unique vector whose initial point coincides with the initial point of v and whose terminal point coincides with the terminal point of w.

Addition Properties § Vector addition is commutative & associative § v + 0 = 0 + v = v § v + (-v) = 0 § v – w = v + (-w)

Vector Multiplication If α is a scalar and v is a vector, the scalar product αv is defined as follows: 1. If α > 0, the product is the vector whose magnitude is α times the magnitude of v and whose direction is the same as v. 2. If α < 0, the product is the vector whose magnitude is the absolute value of α times the magnitude of v and whose direction is opposite that of v. 3. If α = 0 or if v = 0, then αv = 0.