Find the angle between the vector $straight i with hat on top minus straight j with hat on top space and space straight j with hat on top space minus space straight k with hat on top.$

$Let space straight a with rightwards arrow on top space equals space straight i with hat on top minus stack straight j semicolon with hat on top space space straight b with rightwards arrow on top space equals space straight j with hat on top space minus space straight k with hat on top straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space left parenthesis straight i with hat on top minus straight j with hat on top right parenthesis space left parenthesis straight j with hat on top space minus space straight k with hat on top right parenthesis space equals space 1 cross times 0 space plus left parenthesis negative 1 right parenthesis cross times 1 space plus 0 space cross times left parenthesis negative 1 right parenthesis space equals space minus 1 open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of 1 squared plus left parenthesis negative 1 right parenthesis squared plus 0 squared end root space equals square root of 2 open vertical bar straight b with rightwards arrow on top close vertical bar space equals square root of 0 squared plus 1 squared plus left parenthesis negative 1 right parenthesis squared end root space equals square root of 2 We space know space that space straight a with rightwards arrow on top. straight b with rightwards arrow on top space equals open vertical bar straight a with rightwards arrow on top close vertical bar open vertical bar straight b with rightwards arrow on top close vertical bar cos space straight theta Thus comma space cosθ space equals space fraction numerator straight a with rightwards arrow on top. straight b with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar. open vertical bar straight b with rightwards arrow on top close vertical bar end fraction space equals space fraction numerator negative 1 over denominator square root of 2 cross times square root of 2 end fraction equals fraction numerator negative 1 over denominator 2 end fraction rightwards double arrow space space space cosθ space equals space cos 120 degree rightwards double arrow space space space space straight theta space equals space 120 degree$

960 Views

Vector Algebra

Hope you found this question and answer to be good. Find many more questions on Vector Algebra with answers for your assignments and practice.

Mathematics Part II

Browse through more topics from Mathematics Part II for questions and snapshot.