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find the vector which is perpendicular to both A and B but have magnitude equal to that of B A=3i^-2j^,b=4i^+3j^-k^

Asked by anjanajyothi1234 | 19 Jun, 2022, 08:05: AM

Expert Answer

begin mathsize 14px style A with rightwards arrow on top space equals space left parenthesis space 3 space i with hat on top space minus space 2 space j with hat on top space space right parenthesis end style

begin mathsize 14px style B with rightwards arrow on top space equals space left parenthesis space 4 space i with hat on top space plus space 3 space stack j space with hat on top minus space k with hat on top space right parenthesis end style

Vector that is perpendicular to

begin mathsize 14px style A with rightwards arrow on top end style

and

begin mathsize 14px style B with rightwards arrow on top end style

is (

begin mathsize 14px style A with rightwards arrow on top end style

begin mathsize 14px style B with rightwards arrow on top end style

)

begin mathsize 14px style A with rightwards arrow on top space cross times space B with rightwards arrow on top space equals space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row 3 cell negative 2 end cell 0 row 4 3 cell negative 1 end cell end table close vertical bar space equals space 2 space i with hat on top space plus space 3 space j with hat on top space plus 17 space k with hat on top space end style

Vector

begin mathsize 14px style C with rightwards arrow on top end style

that is perpendicular to

begin mathsize 14px style A with rightwards arrow on top end style

and

begin mathsize 14px style B with rightwards arrow on top end style

and of magnitude of

begin mathsize 14px style B with rightwards arrow on top end style

is given as

begin mathsize 14px style C with rightwards arrow on top space equals space fraction numerator open vertical bar B with rightwards arrow on top close vertical bar over denominator open vertical bar A with rightwards arrow on top space cross times space B with rightwards arrow on top close vertical bar end fraction open parentheses A with rightwards arrow on top space cross times space B with rightwards arrow on top close parentheses end style

begin mathsize 14px style open vertical bar B with rightwards arrow on top close vertical bar space equals space square root of 4 squared plus 3 squared plus 1 squared end root space almost equal to space 5.1 end style

begin mathsize 14px style open vertical bar A with rightwards arrow on top space cross times space B with rightwards arrow on top close vertical bar space equals space square root of 2 squared plus 3 squared plus 17 squared end root space almost equal to space 17.4 end style

begin mathsize 14px style C with rightwards arrow on top space equals space fraction numerator 5.1 over denominator 17.4 end fraction space open parentheses 2 space i with hat on top space plus space 3 space j with hat on top space plus space 17 space k with hat on top close parentheses space equals space stretchy left parenthesis 0.586 space i with hat on top space plus space 0.879 space j with hat on top space plus space 4.983 space 17 space k with hat on top stretchy right parenthesis end style

Answered by Thiyagarajan K | 19 Jun, 2022, 08:57: AM

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