यदि `overset to a, oversetto b ,overset to c ` तीन सदिश हो तो सिद्ध कीजिए की ` [overset to a+oversetto boversetto b +overset to c overset to c +oversetto a ] =2 [ oversetto a overset to b overset to c ] `

Explanation

बाँया पक्ष `= [oversetto a + oversetto b oversetto b +overset to c oversetto c +overset to a ]`
` (oversetto a +overset to b )*[(oversetto b+overset to c )xx(oversetto c+oversetto a ) ]`
` " "=(overset to a+overset to b )*[overset to bxxoverset to c +overset to b xxoverset to a +overset to c xxoverset to c +overset to c xxoverset to a ]`
` =(overset to a +overset to b) *[overset to bxxoverset to c -overset to a xxoverset to b + 0+overset to c xxoverset to a ]`
`" "(because overset to axxoverset tob =-overset to b xxoverset to a ("तथा") overset to c xxoverset to c =0) `
` = (overset to a +overset to b )*[overset to bxxoverset to c -overset to a xxoverset to b+ overset to c xxoverset to a ]`
` =overset to a *(overset to b xxoverset to c ) -overset to a *(overset to a xxoverset to b ) +overset to a *(overset toc xxoverset to a )+ overset to b *(overset to b xxoverset to a ) `
`" "- oversettob *(oversetto axxoversettob )+ oversetto b*(oversetto c xxoversetto a ) `
` = (oversetto a overset to b overset toc )-(overset toa overset toa overset tob) +(overset to aoverset to coverset to a )+ (overset to boverset to boverset toc ) - (overset to boverset to boverset to b ) +(overset to b overset tocoverset toa ) `
` = (overset to aoverset to b overset toc ) -0+0+0-0+(overset to b overset to c overset toa ) `
` [because (overset to aoverset to aoverset tob )= (overset toa overset tocoverset toa) =(overset to boverset tob overset toc)= (overset toboverset toaoverset tob)=0]`
`=(oversetto aoversettob oversettoc) +(oversettoboversetto coversettoa ) `
` = (oversettoaoversettoboversettoc)+(overset to aoversettob oversettoc) `
` = 2(oversettoaoversettoboversettoc ) `
= दाँया पक्ष