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Linear Algebra With Applications
Found in: Page 215
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Find the angle θ between each of the pairs of vectors u and v in exercises 4 through 6.

4. u=[11],v=[711] .

The angle θ between u and v is about 12.58° .

See the step by step solution

Step by Step Solution

Step 1: Angle between two vectors

Consider two nonzero vectors x and role="math" localid="1659434098948" y in Rn. The angle between these vectors

Is defined as:

role="math" localid="1659434271678" θ=arccosx.y||x||.||y||

Step 2: Substitute the values into the angle formula

θ=arccosu.v||u||.||v|| =arccos117111-1+1-17-7+11-11 =arccos1-7+1-111+149+121 =arccos18340 =arccos1818.44 =arccos0.976 12.58°

Hence, the value of θ is about 12.58° .


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