Question

$If space straight a with rightwards arrow on top equals 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top comma then space find space straight a space vector space parallel space to space the space vector space straight a with rightwards arrow on top plus straight b with rightwards arrow on top.$

Solution

Given comma straight a with rightwards arrow space on top equals space 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top space and space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top therefore space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space equals space open parentheses 4 space straight i with hat on top space minus straight j with hat on top plus space straight k with hat on top close parentheses space plus space open parentheses 2 space straight i with hat on top space minus 2 straight j with hat on top plus space straight k with hat on top close parentheses equals 6 space straight i with hat on top space minus space 3 straight j with hat on top space plus space 2 straight k with hat on top unit space vector space parallel space to space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis space space equals space fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top over denominator vertical line straight a with rightwards arrow on top plus straight b with rightwards arrow on top vertical line end fraction equals space fraction numerator 6 space straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top over denominator square root of 36 plus 9 plus 4 end root end fraction equals space fraction numerator 6 space straight i with hat on top minus 3 straight j with hat on top plus 2 straight k with hat on top over denominator square root of 49 end fraction equals fraction numerator 6 space straight i with hat on top over denominator 7 end fraction minus fraction numerator 3 straight j with hat on top over denominator 7 end fraction plus fraction numerator 2 straight k with hat on top over denominator 7 end fraction

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Vector Algebra

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