1. 10.3 Vector Valued Functions
By Loni Dagan, 3/28/02
Greg Kelly, Hanford High School, Richland, Washington

2. Any vector can be written as a linear combination of two standard unit vectors.
The vector v is a linear combination of the vectors i and j.
The scalar a is the horizontal component of v and the scalar b is the vertical component of v.

3. We can describe the position of a moving particle by a vector, r(t).
If we separate r(t) into horizontal and vertical components, we can express r(t) as a linear combination of standard unit vectors i and j.

4. In three dimensions the component form becomes:

5. Graph on the TI-89 using the parametric mode.2
ENTER Y=
ENTER
WINDOW
GRAPH

6. Graph on the TI-89 using the parametric mode.2
ENTER Y=
ENTER
WINDOW
GRAPH

7. Most of the rules for the calculus of vectors are the same as we have used, except:
“Absolute value” means “distance from the origin” so we must use the Pythagorean theorem.

8. Example 5:
a) Find the velocity and acceleration vectors.
b) Find the velocity, acceleration, speed and direction
of motion at

9. Example 5:
b) Find the velocity, acceleration, speed and direction
of motion at
velocity:
acceleration:

10. Example 5:
b) Find the velocity, acceleration, speed and direction
of motion at
speed:
direction:

11. Example 6:
a) Write the equation of the tangent where
At :
position:
slope:
tangent:

12. p Example 6: b) Find the coordinates of each point on the path where
the horizontal component of the velocity is 0.
The horizontal component of the velocity is p