Chapter 6 6.3 – 6.5 Vectors

6.3 Vectors in the Plane Component Form of a Vector Vectors have an Initial Point and a Terminal Point. They travel in a direction. LABELS: u, v, w or To have equivalent vectors, you must have the same slope and the same magnitude. Magnitude is the length. Component Form of a Vector v – Standard Position Initial Pt. (0, 0) to Terminal Pt. v = Magnitude = Magnitude=1, Unit Vector Given 2 points, Find Component Form Magnitude???

6.3 cont’d. Example: Find Component Form and Magnitude of Basic Vector Operations Given: Finding Unit Vectors: Find: 2v w – v v + 2w 3w – 5v Length = 1, Example Standard Unit Vectors Is the same as: EXAMPLES…….

6.4 Vectors and Dot Products Properties p.422, please look at them!!!!! Examples, find the Dot Product Given: Magnitude = Find: Angle between 2 vectors Vectors are orthogonal if dot product is zero. Parallel???? Find angle btwn

6.5 Trig. Form of a Complex Number Complex plane – real axis and imaginary axis Absolute Value of a complex number is its length. Example: Plot -2 +5i and find its absolute value. Trigonometric Form: is the same as r is the modulus of z and is the argument of z. Where: go to Trig Form go to Complex Form Examples: Properties p. 434, if you need them I will give them to you.