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

$Two vectors \vec{a} and \vec{b} are parallel and$ $have same magnitude . Then they$ $(1) have same direction, but they are$ $not equal$ $(2) are equal$ $(3) are not equal$ $(4) may or may not be equal$
Commented by Tinkutara last updated on 05/Jun/17

$Answer is (2) . But how ?$
Commented by ajfour last updated on 05/Jun/17

$\bar{a} = r (\sin ϕ \cos θ \hat{i} + \sin ϕ \sin θ \hat{j} + \cos ϕ \hat{k})$ $\bar{b} = r (\sin ϕ \cos θ \hat{i} + \sin ϕ \sin θ \hat{j} + \cos ϕ \hat{k})$ $s o, \bar{a} = \bar{b}; (r, θ, ϕ) c a n n o t b e$ $c o m p e n s a t e d f o r .$
Commented by Tinkutara last updated on 05/Jun/17

$But their directions can be opposite . In$ $that case \vec{a} \neq \vec{b}, rather \vec{a} = - \vec{b} . In this$ $case also ∣ \vec{a} ∣ = ∣ \vec{b} ∣ . So in my view,$ $answer should be (4) .$
Commented by mrW1 last updated on 05/Jun/17

$t h e a n s w e r s h o u l d b e (4) .$
Commented by Tinkutara last updated on 05/Jun/17

$Thanks Sir!$
Commented by ajfour last updated on 05/Jun/17

$t b e r e i s a w o r d a n t i p a r a l l e l, w e$ $u s e i t f o r v e c t o r s, n o t f o r l i n e s . .$
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