Home
Class 12
MATHS
If overset(to)(A), overset(to)(B), overs...

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)))=.........`

Text Solution

Verified by Experts

The correct Answer is:
0
`(vec(A).(vec(B)xxvec(C)))/((vec(C)xxvec(A))"."vec(B)) + (vec(B)(vec(A)xxvec(C)))/(vec(C).(vec(A)xxvec(B)))`
`=([vec(A)vec(B)vec(C)])/([vec(C)vec(A)vec(B)])+[[vec(B)vec(A)vec(C)]]/[[vec(C)vec(A)vec(B)]]=[[vec(A)vec(B)vec(C)]-[vec(A)vec(B)vec(B)]]/[[vec(C)vec(A)vec(B)]]=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

if overset(to)(b) " and " overset(to)(c ) are any two non- collinear unit vectors and overset(to)(a) is any vector then (overset(to)(a).overset(to)(b))overset(to)(b).(overset(to)(a).overset(to)(c )) overset(to)(c ) + .(overset(to)(a).(overset(to)(b)xxoverset(to)(c)))/(|overset(to)(b)xxoverset(to)(c)|^(2)).(overset(to)(b)xxoverset(to)(c))=.........

If overset(to)(a) , overset(to)(b) " and " overset(to)( c) are unit coplanar vectors then the scalar triple product [2 overset(to)(a) - overset(to)(b), 2 overset(to)(b) - overset(to)(c ) ,2 overset(to)(c ) - overset(to)(a)] is

if overset(to)(a), overset(to)(b) " and " overset(to)(c ) are unit vectors satisfying |overset(to)(a)-overset(to)(b)|^(2)+|overset(to)(b)-overset(to)(c)|^(2)+|overset(to)(c)-overset(to)(a)|^(2)=9 |2overset(to)(a) +5overset(to)(b)+5overset(to)(c)| is equal to

Let overset(to)(u),overset(to)(v) " and " overset(to)(w) be vectors such that overset(to)(u)+overset(to)(v)+overset(to)(w)=overset(to)(0). If |overset(to)(u)|=3.|overset(to)(v)|=4" and " |overset(to)(w)|=5 " then " overset(to)(u).overset(to)(v)+overset(to)(v).overset(to)(w)+overset(to)(w).overset(to)(u) is

If overset(to)(a),overset(to)(b),overset(to)(c ),overset(to)(d) are four distinct vectors satisfying the conditions overset(to)(a)xxoverset(to)(b)=overset(to)(c )xx overset(to)(d) " and " overset(to)(a)xxoverset(to)(c ) = overset(to)(b)xx overset(to)(d) then prove that , overset(to)(a).overset(to)(b)+overset(to)(c ). overset(to)(d) ne overset(to)(a). overset(to)(c)+overset(to)(b).overset(to)(d) .

If overset(to)(a) , overset(to)(b) , overset(to)(c ) " and " overset(to)(d) are the unit vectors such that (overset(to)(a)xx overset(to)(b)). (overset(to)(c )xx overset(to)(d)) =1 " and " overset(to)(a), overset(to)(c ) = .(1)/(2) , then

If overset(to)(X) "." overset(to)(A) =0, overset(to)(X) "." overset(to)(B) =0, overset(to)(X) "." overset(to)(C ) =0 for some non-zero vector overset(to)(X) " then " [overset(to)(A) overset(to)(B) overset(to)(C )]=0