5.4 Vector Triangles
A vector is a quantity that has both ______________________ and _______________________.
Vocab

We represent vectors with an arrow that have an ______________ point and a ______________ point.

The _______________ of a vector is the angle between the vector and the positive x-axis.

The length of the line segment represents the ____________________ of the vector.

___________________ vectors have the same magnitude and direction.

___________________ vectors have the same magnitude but opposite direction.

___________________ vectors have the same or opposite direction but not necessarily the same
magnitude.
Ex. 1
a) label the initial point
d) draw 2 parallel vectors
b) label the terminal point
e) estimate the direction
c) draw its opposite vector
f) estimate the magnitude
a) label the initial point
d) draw 2 parallel vectors
b) label the terminal point
e) estimate the direction
c) draw its opposite vector
f) estimate the magnitude
Ex. 2
Vector Addition (Resultant Vector)
Geometric Representations
+
1) End-to-End Method
2) Parallelogram Method
Ex. 3 Find the resultant vector using both the end-to-end method and the parallelogram method.
a)
b)
+
+
When you add opposite vectors the resultant is the _____________________________.
Multiplying Vectors by a Scalar
Let
v=
Ex. 4 Let
then, 2v =
a=
b=
a) a – b =
-v =
½v=
c=
b) 3a + c =
c) 3b + c
Try to draw a vector representation of each of the following scenarios.
a) A car traveling at 42 mi/h due west
b) A wind blowing a sailboat in the direction of S63°W with a gale force of 46.1 mi/h
c) An object with mass 850 kg on an inclined plane
d) A person lifting a 130-lb weight by using a pulley and a rope being pulled through the pulley at a 42°
angle from vertical
What do these all have in common?