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Question Number 19857 by Nayon last updated on 16/Aug/17

$$proofthat(\underset{-}{a}+\underset{-}{b}).\underset{-}{c}=\underset{-}{a}.\underset{-}{c}+\underset{-}{b}.\underset{-}{c}$$$$orthedistribiutinglawofdotproducts$$$$$$

Commented by Nayon last updated on 16/Aug/17

$$mrw1plsexplain$$

Commented by mrW1 last updated on 16/Aug/17

$$(\mathbf{a}+\mathbf{b})\cdot \mathbf{c}=\mid \mathbf{a}+\mathbf{b}\mid \times \cos \theta \times \mid \mathbf{c}\mid$$$$=\mathrm{PQ}\times \mid \mathbf{c}\mid$$$$=(\mathrm{PQ}+\mathrm{QR})\times \mid \mathbf{c}\mid$$$$=(\mid \mathbf{a}\mid \times \cos {\theta }_1+\mid \mathbf{b}\mid \times \cos {\theta }_2)\times \mid \mathbf{c}\mid$$$$=\mid \mathbf{a}\mid \times \cos {\theta }_1\times \mid \mathbf{c}\mid +\mid \mathbf{b}\mid \times \cos {\theta }_2\times \mid \mathbf{c}\mid$$$$=\mathbf{a}\cdot \mathbf{c}+\mathbf{b}\cdot \mathbf{c}$$

Commented by mrW1 last updated on 16/Aug/17

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