a-1-b-2-a-b-pi-3-a-b-

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

∣ \vec{a} ∣= 1

∣ \vec{b} ∣= 2

∢ (\vec{a}, \vec{b}) = \frac{π}{3}

∣ \vec{a} + \vec{b} ∣= ?

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

\vec{a} . \vec{b} = 1.2 . c o s \frac{π}{3} = 1

∣ \vec{a} + \vec{b} ∣= \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

∣ a + b ∣^{2} = 1^{2} + 2^{2} - 2 \times 1 \times 2 \cos (π - \frac{π}{3})

∣ a + b ∣^{2} = 1^{2} + 2^{2} + 2 \times 1 \times 2 \cos (\frac{π}{3})

∣ a + b ∣^{2} = 1^{2} + 2^{2} + 2 \times 1 \times 2 \times \frac{1}{2}

∣ a + b ∣^{2} = 7

∣ a + b ∣= \sqrt{7}

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