Precalculus
8.1 (day 1) Introduction to Vectors (notes part 1)
Name: _________________________________
Period: ______
Questions 1 – 4: Use the vectors below to graph the indicated vectors. Use the grid provided.
1) v  z
2) 2u  w
1
2
3) u  w  v
4) The resultant vector below was created from two of the given vectors. Define the vector equation that creates this
resultant vector.
Review of Law of Sines & Law of Cosines
Used when given the
following arrangements
of sides/angles:
AAS, ASA, SSA
Used when given the
following arrangements
of sides/angles:
SAS, SSS
Questions 1 – 2: Use the appropriate law to find the missing measure.
1)
2)
3) Find m∠B from #2
Precalculus
8.1 (day 1) Introduction to Vectors (notes part 2)
Name: _________________________________
Period: ______
Definitions
vector: A quantity that possesses magnitude and direction
scalar: any real number (no indication of direction)
Standard Position for Vectors:
θ
Vector Operations
 Addition – tip-to-tail

Subtraction – change the problem to addition of the opposite

Scalar multiplication – Multiply the magnitude of the vector, keep the direction the same.
Applications
1) Heather is pushing the handle of a lawn mower with a force of 450 Newtons at an angle of 56° with the ground.
a) Draw a diagram that shows the resolution of the force that Heather exerts into its rectangular components.
b) Find the magnitudes of the horizontal and vertical components of the force.
2) While playing a golf video game, Ana hits a ball 35 degrees above the horizontal at a speed of 40 miles per hour with
a 5 miles per hour wind blowing, as shown. Find the resulting speed and direction of the ball.