10.3 Vector Valued Functions

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Presentation transcript:

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

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.

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.

In three dimensions the component form becomes:

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

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

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.

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

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

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

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

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