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if vector P +vector Q = vector R and vector P vector - vector Q = vector S , then R²+S² is equal to

Asked by mrudhulaprakashmanda844 13th July 2022, 8:39 PM
Answered by Expert
Answer:
begin mathsize 14px style R with rightwards arrow on top space equals space P with rightwards arrow on top space plus space Q with rightwards arrow on top end style
begin mathsize 14px style R squared space equals space R with rightwards arrow on top space times space space R with rightwards arrow on top space equals space open parentheses P with rightwards arrow on top space plus space Q with rightwards arrow on top close parentheses times open parentheses P with rightwards arrow on top space plus space Q with rightwards arrow on top close parentheses space end style
begin mathsize 14px style R squared space equals space P squared plus Q squared plus 2 space space P with rightwards arrow on top space times space space Q with rightwards arrow on top end style     ...............................(1)
begin mathsize 14px style S with rightwards arrow on top space equals space P with rightwards arrow on top space minus space Q with rightwards arrow on top end style
begin mathsize 14px style S squared space equals space S with rightwards arrow on top space times space space S with rightwards arrow on top space equals space open parentheses P with rightwards arrow on top space minus space Q with rightwards arrow on top close parentheses times open parentheses P with rightwards arrow on top space minus space Q with rightwards arrow on top close parentheses space end style
begin mathsize 14px style S squared space equals space P squared plus Q squared minus 2 space space P with rightwards arrow on top space times space space Q with rightwards arrow on top end style  ..................................(2)
By adding eqn.(1) and eqn.(2), we get

begin mathsize 14px style R squared plus S squared space equals space 1 half open parentheses P squared plus Q squared close parentheses end style
Answered by Expert 13th July 2022, 9:27 PM
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