find the component of 3i+4j along i+j ?

Asked by puneetgarg2555 | 27th May, 2018, 07:56: AM

Expert Answer:

Component of vector A on vector B is given by,
 
 c o m p o n e n t space o f space A equals space fraction numerator A with rightwards arrow on top. space B with rightwards arrow on top over denominator stack open vertical bar B close vertical bar with rightwards arrow on top end fraction

A with rightwards arrow on top. space B with rightwards arrow on top space equals space space left parenthesis 3 i with hat on top plus 4 j with hat on top right parenthesis space. left parenthesis space i with hat on top plus j with hat on top right parenthesis space equals space 3 left parenthesis 1 right parenthesis space plus space 4 space left parenthesis 1 right parenthesis space equals space 7 space
open vertical bar B with rightwards arrow on top close vertical bar space equals square root of 1 squared plus 1 squared end root equals space square root of 2

fraction numerator begin display style A with rightwards arrow on top. space B with rightwards arrow on top end style over denominator begin display style stack open vertical bar B close vertical bar with rightwards arrow on top end style end fraction equals space fraction numerator 7 over denominator square root of 2 end fraction

T h u s comma space fraction numerator begin display style 7 end style over denominator begin display style square root of 2 end style end fraction space i s space c o m p o n e n t space o f space v e c t o r space A space a l o n g space v e c t o r space B. space
space

Answered by Shiwani Sawant | 28th May, 2018, 12:36: PM