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The Question

$\angle$ between $\vec{a}$ and $\vec{b}$ is $60^{\circ}$. If $|a|=3$ and $|b|=5$, find $|a+b|$ and $|a-b|$. Hint use law of cosines

Before I used law of cosines, I did something like below, but didn't get the right asnwer:

Is the method wrong or something?

1 Answers 1

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You have done exactly correct up to $|a+b|^2=(\frac{3\sqrt{3}}{2})^2+(5+\frac{3}{2})^2$. Then you done the mistake as $(5+\frac{3}{2})^2=(\frac{13}{2})^2=\frac{169}{4}$ and you have written $16$.

BTW, your question has given hint to use cosine law, and the label says without cosine.

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    @jiewmeng: I meant I like drawing the figure, labels, no step jump, all calculation in rough in the right side (like you did). So, looking at your answer sheet, I remembered my school days. I did e$x$actly like you (of course those silly mistakes, which people now say "typo"). Alas, I lost those good habits later which has lead me to making typos very often!2011-11-11