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If the scalar product of the vector hati+hatj+2hatk with the unti vector along mhati+2hatj+3hatk is equal to 2, then one of the value of m is

Answer»

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Solution :`(hati +hatj +2 hatk). ((mhati +2hatj +3hatk )/( SQRT(m^(2)+2^(2)+3^(2))))=2`
`implies m+2+6=2sqrt(13+m^(2))`
`implies (m+8)^(2)=4(13+m^(2))`
`implies m^(2)+16M+64 =4M^(2)+52`
` implies 3m^(2)-16m - 12=0 `
`implies(3m+2)(m-6)=0`
`implies m=6,-(2)/(3)`


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