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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 in exercises 4 through 6.

5. u=[123V=234] .

The angle θ between u and v is about 0.1 2 1 9 radians.

See the step by step solution

Step by Step Solution

Step 1: Correlation coefficient

The correlation coefficient r between two characteristics of a population is the

Cosine of the angle between the deviation vectors x and y for the two characteristics:


 Step 2: Substitute the values into the angle formula

The given vectors are u=123 and v=234.

The angle formula role="math" localid="1659426804326" θ=cos-1=x.y||u||.||v||.

Find u.v and ||u||.||v||

u.v=123.234 =1×2+3+3×4 =20


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

θ=cos-1 2014.29 0.1219

Hence, the value of θ is about 0.1219 radians.

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