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Maths-

General

Easy

Question

If $stack a with minus on top comma stack b with minus on top comma stack c with minus on top$ be the three vectors such that $stack a with minus on top cross times stack b with minus on top equals stack c with minus on top text and end text stack b with bar on top cross times stack c with bar on top equals stack a with bar on top$ then

$| \bar{a} | = | \vec{b} | = | \bar{c} | = 1$
$| \bar{a} | = | \bar{b} | = | \bar{c} | \neq 1$
$\bar{a}, \bar{b}, \bar{c}$ are orthogonal in pairs
$| \bar{a} | \neq | \bar{b} | \neq | \bar{c} |$

The correct answer is: $stack a with minus on top comma stack b with minus on top comma stack c with minus on top$ are orthogonal in pairs

$table row cell stack a with minus on top cross times stack b with minus on top equals stack c with minus on top therefore stack c with bar on top text end text text i end text text s end text text end text perpendicular r stack a with bar on top text end text text a end text text n end text text d end text text end text stack b with bar on top text end text text , end text text end text text a end text text l end text text s end text text o end text text end text end cell row cell stack b with bar on top cross times stack c with bar on top equals stack a with bar on top therefore stack a with bar on top text end text text i end text text s end text text end text perpendicular r stack b with bar on top text end text text a end text text n end text text d end text text end text stack c with bar on top end cell row cell therefore stack a with minus on top comma stack b with minus on top comma stack c with minus on top text end text text a end text text r end text text e end text text end text text m end text text u end text text t end text text u end text text a end text text l end text text l end text text y end text text end text text p end text text e end text text r end text text p end text text e end text text n end text text d end text text i end text text c end text text u end text text l end text text a end text text r end text text end text end cell end table$

Related Questions to study

If $stack a with minus on top equals stack i with minus on top plus stack j with minus on top plus stack k with minus on top comma stack b with minus on top equals stack i with minus on top minus stack j with minus on top plus stack k with minus on top$ then $stack i with minus on top cross times open square brackets open parentheses stack a with minus on top cross times stack b with minus on top close parentheses cross times stack i with minus on top close square brackets plus stack j with minus on top cross times open square brackets open parentheses stack a with minus on top cross times stack b with minus on top close parentheses cross times stack j with minus on top close square brackets plus stack k with minus on top cross times open square brackets open parentheses stack a with minus on top cross times stack b with minus on top close parentheses cross times stack k with minus on top close square brackets equals$

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