4-4-16 T4.1a To Define and Use Vectors Don’t worry about getting a calculator today, but you will need one tomorrow.  Got ID?

Lesson: Start copying: Vectors A vector is a directed line segment with magnitude (newtons, pounds, miles per hour, etc.) and direction. P (terminal point) Magnitude 30 O (initial point) Horizontal Vectors can be written in bold: OP or with an arrow above it OP, or with a capital letter “A” or a lowercase letter “a” Two vectors are equal if and only if they have the same magnitude and direction.

These two vectors are equal, that is, the magnitudes and directions are the same on both. These are not A scalar multiplication can be applied to vectors. For example, this is 2A.

If this is a: Then ½ a is: a If this is a: Then (– a) is: -a Notice these have the same magnitude, but the direction is 180° away!

A + B can be shown in two ways: A and B are the components B A Resultant vector of A + B B A Although this is true, we will use the next method:

The Parallelogram Rule for A + B represents two forces acting on a point. If we have: A B terminal B’ Resultant vector of A + B A’ Then A + B is put together like this: A B initial Notice the directions: THIS IS VERY IMPORTANT!!! Notice that the RESULTANT IS ALSO A VECTOR!!!

Also, b – a = b + (-a) a b initial -a b + (-a) b -a’ b’ terminal

This is the same as the top of your sheet: b c d e f h g 5) -b 8) 2h 11) h + g (use P.R.) h b h’ h + g g’ -b h g h

How would you do #20? a b c e h g f d 14) b + d (use P. R.) 17) a – c (use P. R.) a + (– c) c a b’ d’ –c’ d b b + d a + (– c) –c a’ How would you do #20?

What do you notice about #21 & 22? 20. (a + b) + c b c c’ b’ (a +b)’ (a +b) a’ a (a +b) + c (a +b) c b What do you notice about #21 & 22?

Use the Parallelogram Rule for all additions and subtractions. Active Learning Assignment: Vector I Handout: 6-22 Col. 2, 3 Use the Parallelogram Rule for all additions and subtractions. WOW: Your life can turn on a dime—for better or worse. Small decisions can have great impacts!