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10.3 Vector Valued Functions

10.3 Vector Valued Functions. 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 .

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10.3 Vector Valued Functions

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  1. 10.3 Vector Valued Functions 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. 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. We can describe the position of a moving particle by a vector, r(t).

  4. In three dimensions the component form becomes:

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

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

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

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

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

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

  12. 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 . Example 6: p

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