Length of a vector difference

Two vectors satisfy $\|a\| = 5$ , $\|b\| = 3$ , and $\|a + b\| = 7$ . Find $\|a - b\|$ . (to 4 decimals)

Show hints (2)+

Expand $\|a+b\|^2 = \|a\|^2 + 2(a\cdot b) + \|b\|^2$ to solve for $a\cdot b$ first.
Then $\|a-b\|^2 = \|a\|^2 - 2(a\cdot b) + \|b\|^2$ - flip the sign on the cross term.

Answer

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4.3589 (± 0.001)

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude