If `overset(to)(A), overset(to)(B), overset(to)(C )` three non-coplanar vectors then
`(overset(to)(A) ,(overset(to)(B)xxoverset(to)(C)))/((overset(to)(C)xx overset(to)(A)). overset(to)(B))+ (overset(to)(B).(overset(to)(A) xx overset(to)(C)))/(overset(to)(C).(overset(to)(A)xx overset(to)(B)))=.........`

For any three vectors overset(to)(a), overset(to)(b) " and " overset(to)(C ) (overset(to)(a) - overset(to)(b)). {(overset(to)(b)-overset(to)(c))xx(overset(to)(c)-overset(to)(a))} = 2overset(to)(a).(overset(to)(b)xx overset(to)(c))

For any three vectors overset(to)(a), overset(to)(b) " and " overset(to)(C ) (overset(to)(a) - overset(to)(b)). {(overset(to)(b)-overset(to)(c))xx(overset(to)(c)-overset(to)(a))} = 2overset(to)(a).(overset(to)(b)xx overset(to)(c))

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

If overset(to)(a) , overset(to)(b) " and " overset(to)(c ) are three non- coplanar vectors then (overset(to)(a) + overset(to)(b) + overset(to)(c )) . [( overset(to)(a) + overset(to)(b)) xx (overset(to)(a) + overset(to)(c ))] equals

The scalar overset(to)(A) .[(overset(to)(B) xx overset(to)( C)) xx (overset(to)(A) + overset(to)(B) + overset(to)( C))] equals

If the vectors overset(to)(b), overset(to)(c ) , overset(to)(d) are not coplanar then prove than the vectors (overset(to)(a) xx overset(to)(b)) xx (overset(to)(c ) xx overset(to)(d)) + (overset(to)(a) xx overset(to)(c )) xx (overset(to)(d) xx overset(to)(b)) +(overset(to)(a) xx overset(to)(d)) xx (overset(to)(b) xx overset(to)( c)) is parallel to overset(to)(a)

If overset(to)(A) , overset(to)(B) " and " overset(to)( c) are vectors such that |overset(to)(B) |=|overset(to)( C ) | . Prove that | (overset(to)(A) + overset(to)(B)) xx (overset(to)(A) + overset(to)(C )) | xx (overset(to)(B) xx overset(to)(C )) . (overset(to)(B) + overset(to)( C )) = overset(to)(0)

The scalar overset(to)(A) .[(overset(to)(B) + overset(to)( C)) xx (overset(to)(A) + overset(to)(B) + overset(to)( C))] equals

If vectors overset(to)(a) , overset(to)(b) , overset(to)( C) are coplanar then show that |{:(overset(to)(a),,overset(to)(b),,overset(to)(c )),(overset(to)(a)"."overset(to)(a),,overset(to)(a)"."overset(to)(b),,overset(to)(a)"."overset(to)(c )),(overset(to)(b)"."overset(to)(a),,overset(to)(b)"."overset(to)(b),,overset(to)(b)"." overset(to)(c )):}|