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Vector Algebra

Question
CBSEENMA12033977
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Write two different vectors having same magnitude.

Solution

Let straight a with rightwards arrow on top space equals straight i with hat on top space plus space 2 space straight j with hat on top space plus space 2 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space plus space 2 space straight k with hat on top
therefore space space space space 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 plus left parenthesis 2 right parenthesis squared end root space equals space square root of 1 plus 4 plus 4 end root space equals square root of 9 space equals space 3 space space space space space space space space 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 plus left parenthesis 2 right parenthesis squared end root space equals square root of 4 plus 1 plus 4 end root space equals square root of 9 space equals 3 therefore 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 comma space space space but space straight a with rightwards arrow on top space not equal to space straight b with rightwards arrow on top
as their corresponding components are not equal.

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