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Vector Algebra

Question
CBSEENMA12033978

Write two different vector having same direction.

Solution

Let straight a with rightwards arrow on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top comma space space space space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 3 space straight j with hat on top space plus space 3 space straight k with hat on top
Direction ratios of  straight a with rightwards arrow on top are 1, 1, 1 and direction ratios of straight b with rightwards arrow on top are 3, 3, 3.
 ∴   direction cosines of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are 
                 fraction numerator 1 over denominator square root of 1 plus 1 plus 1 end root end fraction comma space fraction numerator 1 over denominator square root of 1 plus 1 plus 1 end root end fraction comma space fraction numerator 1 over denominator square root of 1 plus 1 plus 1 end root end fraction
and  fraction numerator 3 over denominator square root of 9 plus 9 plus 9 end root end fraction comma space fraction numerator 3 over denominator square root of 9 plus 9 plus 9 end root end fraction comma space fraction numerator 3 over denominator square root of 9 plus 9 plus 9 end root end fraction space respectively.
i.e. fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction space and space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction comma space fraction numerator 1 over denominator square root of 3 end fraction
therefore space space space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top  are different vectors but have the same direction.