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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 angleθ between each of the pairs of vectors u and localid="1659433601917" v in exercises 4 through

6. u=[1-12-2,v =2345]

The angle θ between u and v is about 97.4°.

See the step by step solution

Step by Step Solution

Step 1: Angle between two vectors

Consider two nonzero vectors x and y in Rn. The anglebetween these vectors

Is defined as:


Step 2: Substitute the values into the angle formula

The given vectors are u=1-12-2 and v=2345.

Now, calculate the angle by substituting the required values into the angle formula


localid="1659428200763" θ=arccos(θ)=u.v||u||.||v||=arccos(θ)1-12-2 .234512+(-1)2+22+(-2)122+32+42+52=arccos(θ)1.2-1.3+2.4-2.51+1+4+4 4+9+16+25 =arccos(θ)2-3+8-1010.54=arccos(θ)-354097.4°

Hence, the value of θ is about 97.4°.

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