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Let v and w be two vectors with ||v|| = 3 and ||w|| = 4. What is the largest and smallest possible values of v · w?

I found this question in the textbook and I'm not sure how to solve this since I just started linear algebra. Any help is appreciated.

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    You should mention that you work with a inner product space over the reals.2012-09-21

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We have $||v+w||^2=|| v||^2+ ||w||^2+2(v\cdot w)$. The smallest possible value of $||v+w||^2$ is $1$, when the vectors are pointing in opposite directions, and the largest possible value is $49$, when they point in the same direction.

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    Indeed. Look above. Smallest value of $||v+w||^2$ is 1, so smallest value of $2(v\cdot w)$ is $1-9-16=-24$, so smallest value of $v\cdot w$ is $-24/2$. Largest possible value of $||v+w||^2$ is $49$, so largest value of $2(v\cdo w)$ is $49-9-16=24$. largest value of $v\cdot w$ is $24/2$.2012-09-21