Let $straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top$ and $straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top.$ Is $open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar space ?$ Are the vectors $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ equal?

Solution

straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space plus space straight j with hat on top

open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root space equals space square root of 1 plus 4 end root space equals space square root of 5 open vertical bar straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 2 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 4 plus 1 end root space equals space square root of 5

therefore space space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar

straight a with rightwards arrow on top space and space straight b with rightwards arrow on top

are not equal as their corresponding components are distinct.

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