Before you came along we had no direction

Before you came along we had no direction!! V C E O T S R

A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude and the arrow indicates the direction of the vector. Blue and orange vectors have same magnitude but different direction. Blue and purple vectors have same magnitude and direction so they are equal. Blue and green vectors have same direction but different magnitude. Two vectors are equal if they have the same direction and magnitude (length). Another word for length is NORM

Vectors versus Scalar A vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude Example: the motion of a train is 160 km/hr in a westerly direction Example: the number of passengers on the train is 160

A vector is said to be COLLINEAR to another vector if it is parallel to another vector. Blue and green and purple vectors are COLINEAR…even though they may not be pointing in the same direction

Two vectors are said to be OPPOSITE to each other if they have the same NORM but OPPOSITE direction.

A vector can be named using the two letters that make up its end points: Or it is simply named with a single letter with an arrow over top. Often the letters used are u, v, and w.

The NORM of the vector is denoted by this notation Example: Find

Two vectors that are perpendicular to each other are orthogonal. Blue and purple vectors are ORTHOGONAL

How can we find the magnitude if we have the initial point and the terminal point? The distance formula e d u a it n g Initial Point m is e h t ng le Q Terminal Point is n io e t c e ngl r i d a s i th P How can we find the direction? (Is this all looking familiar? You can make a right triangle and use trig to get the angle!)

The direction is described much like using a protractor Start at the horizontal half-line directed eastward and rotate counter-clockwise As an example, the notation for this is

For the orientation of the vector PQ…

A vector’s direction can also be related to CARDINAL POINTS (what’s on a map!) Ex. 30 degrees West of South (S 30 o W) 60 degrees West of North (N 60 o W) 7 degrees East of North (N 7 o E)

Vectors are equal as long as the direction and magnitude are the same. It does not matter where they are located. It is easiest to find a vector with initial point at the origin and terminal point (x, y). Initial Point P is n io e t c e ngl r i d a s i th Q Terminal Point

OPERATIONS ON VECTORS You can add and subtract vectors!

To Toadd addvectors, we weput putthe theinitialpointof ofthe thesecond vectoron onthe theterminalpointof ofthe thefirstvector. The resultantvectorhas hasan aninitialpointat atthe theinitialpoint of ofthe thefirstvectorand andaaterminalpointat atthe theterminal pointof ofthe thesecondvector(seebelow--bettershown thanput putin inwords). Terminal point of w Initial point of v Move w over keeping the magnitude and direction the same.