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Section 11.1 : Basic Concepts
1. Give the vector for the line segment from \(\left( { - 9,2} \right)\) to \(\left( {4, - 1} \right)\). Find its magnitude and determine if the vector is a unit vector.
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Start SolutionWriting down a vector for a line segment is really simple. Just recall that the components of the vector are always the coordinates of the ending point minus the coordinates of the starting point. Always keep in mind that the starting and ending points are important!
Here is the vector for this line segment.
\[\vec v = \left\langle {4 - \left( { - 9} \right), - 1 - 2} \right\rangle = \require{bbox} \bbox[2pt,border:1px solid black]{{\left\langle {13, - 3} \right\rangle }}\] Show Step 2To compute the magnitude just recall the formula we gave in the notes. The magnitude of this vector is then,
\[\left\| {\vec v} \right\| = \sqrt {{{\left( {13} \right)}^2} + {{\left( { - 3} \right)}^2}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\sqrt {178} }}\] Show Step 3Because we can see that \(\left\| {\vec v} \right\| = \sqrt {178} \ne 1\) we know that this vector is not a unit vector.