Ch. 15- Vectors in 2-D

Simply put, quantities which have only magnitude are called scalars. Quantities that have both magnitude and direction are called vectors. An example of a scalar quantity would be speed. A vector quantity would be velocity. A This vector could be represented by: a a The magnitude (length) could be represented by: O |a|

Two vectors are equal if they have the same magnitude and direction. Since the direction must be the same, equal vectors are parallel as well as equal in length. Negative vectors are parallel and equal in length, but in opposite directions. B B A A is the negative of and

To subtract vectors: We just add its negative! Vector Addition To add vectors a and b: Draw a At the arrowhead end of a draw b Join the beginning of a to the arrowhead end of b to get a + b. b a + b a b a s To subtract vectors: We just add its negative! r r r – s = r + (-s) s r – s -s

Scalar Multiplication If then a -3a If then a So multiplying by a scalar simply lengthens (or shortens) it. If the scalar is negative the new vector has opposite direction.

Component Form of a Vector y is the component form of vector a x -Component form gives us an “algebraic” way to work with vectors. (As opposed to simply using geometric.) If a = and b = then a + b =

Ex. 1 If a = and b = then find a + b:

Using the same p and q, find: If a = then - a = Ex. 2 If p = and q = find q – p: q – p = q + -p Ex. 3 Using the same p and q, find: a) p + 2q b) ½p - 3q

Magnitude (Length) of a Vector If we have the vector: a 3 a = 2 How could we find the magnitude of the vector? If then