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6.4 Vectors and Dot Products

6.4 Vectors and Dot Products. Finding the angle between two vectors Writing a vector as the sum of two vectors components. Definition of Dot Product. Given: Two vectors in Component form The result is a number, not a vector. Find the Dot Product. Given. Find the Dot Product. Given.

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6.4 Vectors and Dot Products

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  1. 6.4 Vectors and Dot Products Finding the angle between two vectors Writing a vector as the sum of two vectors components

  2. Definition of Dot Product Given: Two vectors in Component form The result is a number, not a vector

  3. Find the Dot Product Given

  4. Find the Dot Product Given

  5. Products of the Dot Product

  6. The Angle Between two vectors For angles

  7. The Angle Between two vectors For angles Find the angle between

  8. The Angle Between two vectors For angles Vectors are Orthogonal if there Dot Product (u●v)= 0 What is the angle between the vectors, Why?

  9. Definition of Vector Components Let u and v be nonzero vectors. u = w1 + w2 and w1· w2 = 0 Also, w1 is a scalar of v The vector w1 is the projection of u onto v, So w1 = proj v u w 2 = u – w 1

  10. Decomposing of a Vector Using Vector Components

  11. Decomposing of a Vector Using Vector Components

  12. Decomposing of a Vector Using Vector Components

  13. Definition of Work Work is force times distance. If Force is a constant and not at an angle If Force is at an angle

  14. Homework Page 447 – 448 # 1, 5, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 63, 67

  15. Homework Page 447 – 448 # 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 52

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