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Dot Product of Two Vectors

Dot Product of Two Vectors. ac+bd. Example 1. Example 2. u= v= w=. Angle Between Two Vectors. Example 3. Find the angle between the two vectors. Use the formula to determine the the angle between two vectors whose dot product is zero. ~Flashback~. A=30 º a=12 B=45 º b=

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Dot Product of Two Vectors

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  1. Dot Product of Two Vectors ac+bd

  2. Example 1

  3. Example 2 u= v= w=

  4. Angle Between Two Vectors

  5. Example 3 Find the angle between the two vectors

  6. Use the formula to determine thethe angle between two vectors whose dot product is zero.

  7. ~Flashback~ A=30º a=12 B=45º b= C= c= This is an oblique triangle with what given information? What do you use to solve for the sides? What is angle C and sides b & c ?

  8. 6.4 Finding Vector Components & Work

  9. Added Two vectors

  10. Find the projection of u=<3,5> onto v=<6,2>. Write u as the sum of two orthogonal vectors, one of which is projvu

  11. 1500 lb. boat at a 20 degree incline.

  12. 200 lb. cart on a 30 degree incline.

  13. Work

  14. A force of 45 lbs. in the direction of 30 degrees above the horizontal is required to slide a table across the floor. Find the work done if the table is dragged 20 feet.

  15. 50 lb. force, 12 ft. wide door

  16. 58) A force of 45 pounds in the direction of 30 degrees above the horizontal is required to slide a table across a floor. Find the work done if the table is dragged 20 feet.

  17. 59) A toy wagon is pulled by exerting a force of 20 pounds on a handle that makes a 25 degree angle with the horizontal. Find the work done in pulling the wagon 20 feet.

  18. 60) A mover exerts a horizontal force of 25 pounds on a crate as it is pushed up a ramp that is 12 feet long and inclined at an angle of 20 degrees above the horizontal. Find the work done on the crate.

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