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સદિશનું બીજગણિત

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ગણિત ધોરણ 12 સિમેસ્ટર 4

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ગણિત

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નીચેના સદિશનું માન શોધો :
open parentheses 2 comma space 3 comma space square root of 3 close parentheses


નીચેના સદિશનું માન શોધો :
3 space straight i with hat on top space minus space 4 straight k with hat on top


2 straight i with hat on top space minus space 2 straight j with hat on top space plus space straight k with hat on top  ની દિશામાં એકમ સદિશ શોધો.

20 માનવાળો અને negative 3 straight i with hat on top space plus space 2 square root of 3 space straight j with hat on top space minus space 2 straight k with hat on top  ની દિશાની વિરુદ્ધ દિશાનો સદિશ શોધો.


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stack straight x space with bar on top space equals space 3 straight i with hat on top space plus space 4 straight j with hat on top space minus space 5 straight k with hat on top space space bold અન ે bold space space stack straight y space with bar on top space equals space 2 straight i with hat on top space plus space straight j with hat on top comma, સદિશો માટે stack straight x space with bar on top space plus space 2 stack space straight y space with bar on topની દિશામાં એકમ સદિશ મેળવો.


અહીં, stack straight x space with bar on top space equals space 3 straight i with hat on top space plus space 4 straight j with hat on top space minus space 5 straight k with hat on top space equals space open parentheses 3 comma space 4 comma space minus 5 close parentheses

તથા stack straight y space with bar on top space space equals space 2 straight i with hat on top space plus space straight j with hat on top space equals space open parentheses 2 comma space 1 comma space 0 close parentheses


therefore space stack straight x space with bar on top space plus space 2 space stack straight y space with bar on top space equals space open parentheses 3 comma space 4 comma space minus 5 close parentheses space plus space 2 space open parentheses 2 comma space 1 comma space 0 close parentheses

space space space space space space space space space space space space space space space space space space equals space open parentheses 3 comma space 4 comma space minus 5 close parentheses space plus space open parentheses 4 comma space 2 comma space 0 close parentheses

space space space space space space space space space space space space space space space space space space equals space open parentheses 7 comma space 6 comma space minus 5 close parentheses


therefore space open vertical bar space stack straight x space with bar on top plus space 2 space stack straight y space with bar on top close vertical bar space equals space square root of 7 squared space plus space 6 squared space plus space open parentheses negative 5 close parentheses squared end root

space space space space space space space space space space space space space space space space space space space equals space square root of 49 space plus space 36 plus space 35 end root space equals space square root of 110




therefore space stack straight x space with bar on top space plus space 2 space stack straight y space with bar on top ની દિશામાં એકમ સદિશ


equals space fraction numerator stack straight x space with bar on top plus space 2 space stack straight y space with bar on top over denominator open vertical bar space stack straight x space with bar on top space plus space 2 space stack straight y space with bar on top close vertical bar end fraction


equals space fraction numerator open parentheses 7 comma space 6 comma space minus 5 close parentheses over denominator square root of 110 end fraction


equals space open parentheses fraction numerator 7 over denominator square root of 110 end fraction comma space fraction numerator 6 over denominator square root of 110 end fraction comma space fraction numerator negative 5 over denominator square root of 110 end fraction close parentheses


equals space fraction numerator bold 7 over denominator square root of bold 110 end fraction bold space bold i with bold hat on top bold space bold plus bold space fraction numerator bold 6 over denominator square root of bold 110 end fraction bold space bold j with bold hat on top bold space bold minus bold space fraction numerator bold 5 over denominator square root of bold 110 end fraction bold space bold k with bold hat on top


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