Home
Class 12
MATHS
The scalar overset(to)(A) .[(overset(to...

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

A

0

B

`[overset(to)(A)overset(to)(B)overset(to)(C)]+[overset(to)(B)overset(to)(C) overset(to)(A)]`

C

`[overset(to)(A) overset(to)(B) overset(to)(C)]`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(A) ". " {(vec(B) +vec(C )) xx vec(A) + vec(B) + vec(C ))}`
`[:'" it is a scalar triple product of three vectors of the form " vec(A) , vec(B) + vec(C ) , vec(A) + vec(B) +vec(C )]` ,

`=vec(A) ". " (vec(B) xx vec(A) + vec(B) xx vec(B)`
`+vec(B) xx vec(C ) + vec( C) xx vec(A) + vec( C) xx vec(B) + vec( C) xx vec( C))`
`=vec(A) .(vec(B) xx vec(A)) + vec(A).(vec(B) xx vec(C )) + vec(A). (vec(C) xx vec(B))`
`=[vec(A) vec(B) vec(A)] -[vec(A)vec(B) vec(C )]=0`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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), 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)))=.........

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

Let vec(A),vec(B),vec(C ) be vectors of length 3, 4, 5, respectively Let overset(to)(A) be perpendicular to overset(to)(B) +overset(to)(C ) , overset(to)(B) " to " overset(to)( C) + overset(to)(A) " and " overset(to)(C ) to overset(to)(A) +overset(to)(B) then the length of vector overset(to)(A) +overset(to)(B)+overset(to)(C ) is .......

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

Let overset(to)(a) , overset(to)(b) " and " overset(to)( c) be three non-zero vectors such that no two of them are collinear and (overset(to)(a) xx overset(to)(b)) xx overset(to)( c) = (1)/(3) |overset(to)(b)||overset(to)(c )|overset(to)(a). If 0 is the angle between vectors overset(to)(b) " and " overset(to)(c ) then a value of sin 0 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)(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

Let overset(to)(A),overset(to)(B)" and " overset(to)(C ) be unit vectors . If overset(to)(A).overset(to)(B) = overset(to)(A).overset(to)(C ) =0 and that the angle between overset(to)(B) " and " overset(to)(C )" is " pi//6. Then overset(to)(A) =+-2 (overset(to)(B)xxoverset(to)(C ))