Two-vectors-a-and-b-are-parallel-and-have-same-magnitude-Then-they-1-have-same-direction-but-they-are-not-equal-2-are-equal-3-are-not-equal-4-may-or-may-not-be-equal-

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Question Number 14882 by Tinkutara last updated on 05/Jun/17

$$\mathrm{Two}\mathrm{vectors}\overrightarrow{a}\mathrm{and}\overrightarrow{b}\mathrm{are}\mathrm{parallel}\mathrm{and}$$$$\mathrm{have}\mathrm{same}\mathrm{magnitude}.\mathrm{Then}\mathrm{they}$$$$\left(1\right)\mathrm{have}\mathrm{same}\mathrm{direction},\mathrm{but}\mathrm{they}\mathrm{are}$$$$\mathrm{not}\mathrm{equal}$$$$\left(2\right)\mathrm{are}\mathrm{equal}$$$$\left(3\right)\mathrm{are}\mathrm{not}\mathrm{equal}$$$$\left(4\right)\mathrm{may}\mathrm{or}\mathrm{may}\mathrm{not}\mathrm{be}\mathrm{equal}$$

Commented by Tinkutara last updated on 05/Jun/17

$$\mathrm{Answer}\mathrm{is}\left(2\right).\mathrm{But}\mathrm{how}?$$

Commented by ajfour last updated on 05/Jun/17

$$\overline{a}=r(\sin \varphi \cos \theta \hat{i}+\sin \varphi \sin \theta \hat{j}+\cos \varphi \hat{k})$$$$\overline{b}=r(\sin \varphi \cos \theta \hat{i}+\sin \varphi \sin \theta \hat{j}+\cos \varphi \hat{k})$$$$so,\overline{a}=\overline{b};(r,\theta ,\varphi )cannotbe$$$$compensatedfor.$$

Commented by Tinkutara last updated on 05/Jun/17

$$\mathrm{But}\mathrm{their}\mathrm{directions}\mathrm{can}\mathrm{be}\mathrm{opposite}.\mathrm{In}$$$$\mathrm{that}\mathrm{case}\overrightarrow{a}\ne \overrightarrow{b},\mathrm{rather}\overrightarrow{a}=-\overrightarrow{b}.\mathrm{In}\mathrm{this}$$$$\mathrm{case}\mathrm{also}\mid \overrightarrow{a}\mid =\mid \overrightarrow{b}\mid .\mathrm{So}\mathrm{in}\mathrm{my}\mathrm{view},$$$$\mathrm{answer}\mathrm{should}\mathrm{be}\left(4\right).$$

Commented by mrW1 last updated on 05/Jun/17

$$theanswershouldbe\left(4\right).$$

Commented by Tinkutara last updated on 05/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

Commented by ajfour last updated on 05/Jun/17

$$tbereisawordantiparallel,we$$$$useitforvectors,notforlines..$$

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