तीन सदिशों ` veca , vecb , vecc` के लिए सिद्ध कीजिए कि ` [ veca + vec b " " vec b + vec c " " vec c + vec a]= 2 [ vec a " " vecb" " vecc]`

Explanation

`L.H.S = [ vec a + vecb " " vecb + vecc " " vec c + veca]`
`=( veca + vecb).{( vecb+ vecc) xx ( vec c + veca )}`
`=( veca + vecb ) . { vecb xx vecc + vecbxx veca + vecc xx vecc + vecc xx veca }`
`=( vec a + vecb ) . { vecb xx vecc + vecb xx veca + vec0 + vecc xx veca} `
` ( ,' vec c xx vecc =0 `
`= veca . ( vec b xx vecc ) + vec a. ( vecb xx vec a ) + vec a .( vecc xx veca ) + vecb . ( vecb xx veca )+ vecb . ( veca xx veca )`
` =[ veca " " vecb " " vecc] +[ veca " " vecb" " veca] [ veca " "vecc" " veca] + [ vecb vecb " " vecc] + [ vecb vecb " " veca ]`
` = [ veca " " vecb " " vecc]+ 0+0 +0 +0 +[ veca " " vecb " " vecc] `
` = 2 [ vec a" " vec b" " vecc] ]= R .H.S `