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Question Number 170079 by depressiveshrek last updated on 16/May/22

$$\mid \overrightarrow{a}\mid =1$$$$\mid \overrightarrow{b}\mid =2$$$$\sphericalangle (\overrightarrow{a},\overrightarrow{b})=\frac{\pi }{3}$$$$\mid \overrightarrow{a}+\overrightarrow{b}\mid =?$$

Answered by som(math1967) last updated on 16/May/22

$$\overrightarrow{a}.\overrightarrow{b}=1.2.cos\frac{\pi }{3}=1$$$$\mid \overrightarrow{a}+\overrightarrow{b}\mid =\sqrt{1^2+2^2+2.1}=\sqrt{7}$$

Answered by mr W last updated on 16/May/22

Commented by mr W last updated on 16/May/22

$$\mid a+b{\mid }^2=1^2+2^2-2\times 1\times 2\cos (\pi -\frac{\pi }{3})$$$$\mid a+b{\mid }^2=1^2+2^2+2\times 1\times 2\cos \left(\frac{\pi }{3}\right)$$$$\mid a+b{\mid }^2=1^2+2^2+2\times 1\times 2\times \frac{1}{2}$$$$\mid a+b{\mid }^2=7$$$$\mid a+b\mid =\sqrt{7}$$

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