$find space straight lambda space and space straight mu space if open parentheses straight i with hat on top plus space 3 space straight j with hat on top space plus space 9 space straight k with hat on top close parentheses space space straight x space space left parenthesis 3 space straight i with hat on top plus straight lambda space straight j with hat on top plus space straight mu space straight k with hat on top right parenthesis space equals space 0$

open parentheses straight i with hat on top plus space 3 space straight j with hat on top plus space 9 space straight k with hat on top close parentheses space space straight x space left parenthesis 3 space straight i with hat on top plus straight lambda space straight j with hat on top plus space straight mu space straight k with hat on top right parenthesis space equals 0 open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 1 3 9 row 3 cell negative straight lambda end cell straight mu end table close vertical bar space equals 0 straight i with hat on top left parenthesis 3 straight mu space plus space 9 straight lambda right parenthesis minus straight j with hat on top left parenthesis straight mu minus 27 right parenthesis space plus space straight k with hat on top left parenthesis negative straight lambda minus 9 right parenthesis space equals 0 3 straight mu space plus space 9 straight lambda space equals 0 space space..... space left parenthesis straight i right parenthesis 27 minus straight mu space equals 0 space space space....... left parenthesis ii right parenthesis minus straight lambda minus 9 space equals 0 space...... space left parenthesis iii right parenthesis By space equation space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis space straight mu space equals space 27 space and space straight lambda space equals space minus 9 straight lambda comma space straight mu space value space satisfy space the space equation space left parenthesis straight i right parenthesis so space space straight mu space equals space 27 comma space straight lambda space equals negative 9

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