Advanced Precalculus Notes 8.4 Vectors Vector: a quantity which has both magnitude (represented by length of arrow) and direction. If a vector represents the speed and direction of an object, it is a velocity vector. If it represents direction and amount of force acting on an object it is a force vector. Directed line segment has initial point P 1 and terminal point P 2. The magnitude is the distance from point P 1 to P 2. Zero vector: no magnitude and no direction. Unit vector: A vector with length (magnitude) one, but the same direction as the original vector. The unit vector in the horizontal direction is i and in the vertical direction is j.

Standard position of a vector: initial point is the origin (0, 0) Component form of a vector v: initial point and terminal point vector v = = Magnitude of vector v = Equivalent vectors have the same length (magnitude) and direction. Scalar product: A vector in which each component is multiplied by the scalar, affecting magnitude but not direction.

Find the position vector of the vector if and and graph both the original vector and the position vector.

Vector addition: Read properties of vectors page 609: commutative, associative, additive identity, additive inverse properties.

Let v = and u = find each specified vector, write it in component form, graph it and find its magnitude. a) u + v b) 2u – v c) v + ½ u

Find a unit vector in the direction of v = 4i – 3j A ball is thrown at an initial speed of 25 miles per hour in a direction that makes an angle of 30º with the positive x-axis. Express the velocity vector v in terms of i and j. What is the initial speed in the horizontal direction? What is the initial speed in the vertical direction?

Static Equilibrium: object is at rest and the sum of all forces acting on the object is ZERO. A box of supplies that weighs 1200 pounds is suspended by two cables attached to the ceiling, as shown. What is the tension in the two cables?

Assignment: page 618: 1 – 9, 16 – 22 even, 23, 27, 33, 39, 49, 51, 53, 61, 66