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Section 5-1 : Basic Concepts

  1. Describe the difference between \(\left( {4, - 1} \right)\) and \(\left\langle {4, - 1} \right\rangle \). Illustrate the difference with a sketch.

For problems 2 – 6 give the vector for the set of points. Find its magnitude and determine if the vector is a unit vector.

  1. The line segment from \(\left( {6, - 2,3} \right)\) to \(\left( { - 3, - 2,1} \right)\).
  2. The line segment from \(\displaystyle \left( {1, - \frac{1}{5}} \right)\) to \(\displaystyle \left( {\frac{8}{5},\frac{3}{5}} \right)\).
  3. The line segment from \(\left( {2, - 1,5} \right)\) to \(\left( {8, - 3, - 6} \right)\).
  4. The position vector for \(\left( { - 12,4,8} \right)\).
  5. The position vector for \(\left( {\cos \left( \theta \right),\sin \left( \theta \right)} \right)\) for any angle \(\theta \).
  6. The vector \(\vec v = \left\langle { - 8, - 3} \right\rangle \) starts at the point \(P = \left( {8,2} \right)\). At what point does the vector end?
  7. The vector \(\vec v = \left\langle {0,5, - 3} \right\rangle \) starts at the point \(P = \left( { - 1,0,5} \right)\). At what point does the vector end?
  8. The vector \(\vec v = \left\langle { - 8, - 3} \right\rangle \) ends at the point \(P = \left( {8,2} \right)\). At what point does the vector start?
  9. The vector \(\vec v = \left\langle {4, - 2,1} \right\rangle \) ends at the point \(P = \left( {7, - 7,2} \right)\). At what point does the vector start?