CBSE Class 12-science Answered

Find the unit vector in the direction of $begin mathsize 11px style AB with rightwards arrow on top end style$ , where A and B are the points (2, – 3, 7) and (1, 3, – 4).

Asked by Topperlearning User | 02 Mar, 2015, 09:58: AM

Expert Answer

$begin mathsize 11px style The space position space vector space of space point space straight A space is space begin space mathsize space OA with rightwards arrow on top space equals 2 straight i with hat on top minus 3 straight j with hat on top plus 7 straight k with hat on top space space and space OB with rightwards arrow on top space equals straight i with hat on top plus 3 straight j with hat on top minus 4 straight k with hat on top comma Then space AB with rightwards arrow on top space equals stack space OB with rightwards arrow on top space minus stack space OA with rightwards arrow on top space equals open parentheses straight i with hat on top plus 3 straight j with hat on top minus 4 straight k with hat on top close parentheses minus open parentheses 2 straight i with hat on top minus 3 straight j with hat on top plus 7 straight k with hat on top close parentheses rightwards double arrow AB with rightwards arrow on top space equals negative straight i with hat on top plus 6 straight j with hat on top minus 11 straight k with hat on top Now comma space unit space vector space of space AB with rightwards arrow on top space is AB with rightwards arrow on top equals fraction numerator negative straight i with hat on top plus 6 straight j with hat on top minus 11 straight k with hat on top over denominator square root of open parentheses negative 1 close parentheses squared plus open parentheses 6 close parentheses squared plus open parentheses negative 11 close parentheses squared end root end fraction equals fraction numerator negative straight i with hat on top plus 6 straight j with hat on top minus 11 straight k with hat on top over denominator square root of 158 end fraction end style$