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7.6 Vector Operations Day 1

7.6 Vector Operations Day 1. Do Now Find the distance between the points (-4, -3) and (1, 5). Vector Notation. A vector V whose initial point is the origin and whose terminal point is (a, b) can be written as where a is the horizontal component and b is the vertical component of the vector.

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7.6 Vector Operations Day 1

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  1. 7.6 Vector OperationsDay 1 Do Now Find the distance between the points (-4, -3) and (1, 5)

  2. Vector Notation • A vector V whose initial point is the origin and whose terminal point is (a, b) can be written as where a is the horizontal component and b is the vertical component of the vector

  3. Component Form of a Vector • The component form of a ray AC with and is

  4. Ex • Find the component form of the ray CF if C = (-4, -3) and F = (1, 5)

  5. Length of a Vector • The length, or magnitude, of a vector is given by

  6. Ex • Find the magnitude of vector

  7. Equivalent Vectors • Vectors are equivalent if they have the same magnitude and direction • This means they don’t have to start/end in the same position

  8. Vector Operations • Scalar Multiplication • Vector Addition • Vector Subtraction • Zero Vector

  9. Ex • Evaluate the following, where • 1) u + v • 2) u – 6v • 3) 3u + 4v • 4) |5v – 2u|

  10. Unit Vector • A vector of magnitude 1 is called a unit vector • If v is a vector and is not a zero vector, then a unit vector with the same direction as v is

  11. Ex • Find a unit vector that has the same direction as the vector

  12. Linear Combinations • The unit vectors parallel to the x and y axes are defined as • Any vector can be expressed as a linear combination of unit vectors I and j

  13. Ex • Express vector as a linear combination of I and j

  14. Ex • Write the vector q = -I + 7j in component form

  15. Ex • If a = 5i – 2j and b = -I + 8j, find 3a – b in component form

  16. Direction Angle • The direction angle of a vector is the angle of the triangle created by the vector and the positive half of the x-axis

  17. Ex • Find the direction angle of the vector w = -4i – 3j

  18. Closure • Determine the direction angle of the vector • HW: p.666 #1-57 odds

  19. 7.6 Vector OperationsDay 2 • Do Now • Given the vector • 1) Find the magnitude of u • 2) Find the unit vector that has the same direction • 3) Express the vector as a linear combination of I and j

  20. HW Review: p.666 #1-57 odds

  21. Closure • None • HW: none

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