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10.2 and 10.3

Vectors. 10.2 and 10.3. Most of this is review. Quantities that we measure that have magnitude but not direction are called scalars. Quantities such as force, displacement or velocity that have direction as well as magnitude are represented by directed line segments. B. terminal point.

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10.2 and 10.3

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  1. Vectors 10.2 and 10.3

  2. Most of this is review.

  3. Quantities that we measure that have magnitude but not direction are called scalars. Quantities such as force, displacement or velocity that have direction as well as magnitude are represented by directed line segments. B terminal point The length is A initial point

  4. B terminal point A initial point A vector is represented by a directed line segment. Vectors are equal if they have the same length and direction (same slope).

  5. y A vector is in standard position if the initial point is at the origin. x The component form of this vector is:

  6. y A vector is in standard position if the initial point is at the origin. x The component form of this vector is: The magnitude (length) of is:

  7. The component form of (-3,4) P is: (-5,2) Q v (-2,-2)

  8. Then v is a unit vector. If is the zero vector and has no direction.

  9. Vector Operations: (Add the components.) (Subtract the components.)

  10. Vector Operations: Scalar Multiplication: Negative (opposite):

  11. u v u + v is the resultant vector. u+v (Parallelogram law of addition) v u

  12. 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.

  13. 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).

  14. 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.

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

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

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

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

  19. 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

  20. Homework Page 537 #5-8 b, speed, 9-16 all, 25-28 a,b

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