Three vectors A^(→) , B^(→) and C^(→) add up to zero. Find which is false. (a) (A^(→) ×B^(→) )×C^(→) is not zero unless B^(→) , C^(→) are parallel (b) (A^(→) ×B^(→) )∙C^(→) is not zero unless B^(→) , C^(→) are parallel (c) If A^(→) , B^(→) , C^(→) define a plane, (A^(→) ×B^(→) ×C^(→) ) is in that plane (d) (A^(→) ×B^(→) ).C^(→) = ∣A^(→) ∣∣B^(→) ∣∣C^(→) ∣ → C^2 = A^2 + B^2


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Question Number 19976 by Tinkutara last updated on 19/Aug/17

$Three vectors \vec{A}, \vec{B} and \vec{C} add up to$ $zero . Find which is false .$ $(a) (\vec{A} \times \vec{B}) \times \vec{C} is not zero unless \vec{B}, \vec{C}$ $are parallel$ $(b) (\vec{A} \times \vec{B}) \cdot \vec{C} is not zero unless \vec{B}, \vec{C}$ $are parallel$ $(c) If \vec{A}, \vec{B}, \vec{C} define a plane, (\vec{A} \times \vec{B} \times \vec{C})$ $is in that plane$ $(d) (\vec{A} \times \vec{B}) . \vec{C} = ∣ \vec{A} ∣∣ \vec{B} ∣∣ \vec{C} ∣ \to C^{2} = A^{2} + B^{2}$
	Answered by ajfour last updated on 19/Aug/17

	$(a), (b), (d) a r e f a l s e . f o r (\vec{A} \times \vec{B}) . \vec{C} t o b e$ $z e r o \vec{C} j u s t n e e d t o b e i n t h e p l a n e$ $o f \vec{A} a n d \vec{B} . F o r (\vec{A} \times \vec{B}) \times \vec{C} t o b e$ $z e r o \vec{C} n e e d t o b e p a r a l l e l t o \vec{A} \times \vec{B} .$ $I f (\vec{A} \times \vec{B}) . \vec{C} =∣ \vec{A} ∣∣ \vec{B} ∣∣ \vec{C} ∣, \vec{A}, \vec{B}, \vec{C}$ $j u s t n e e d b e m u t u a l l y p e r p e n d i c u l a r .$
	Commented by ajfour last updated on 19/Aug/17

	$(\hat{i} \times \hat{j}) \times \hat{j} = - \hat{i} . (a) i s f a l s e .$
	Commented by Tinkutara last updated on 20/Aug/17

	$Thank you very much Sir!$
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