`' I '` is the incentre of triangle `A B C` whose corresponding sides are `a , b ,c ,` rspectively. `a vec I A+b vec I B+c vec I C` is always equal to a. ` vec0` b. `(a+b+c) vec B C` c. `( vec a+ vec b+ vec c) vec A C` d. `(a+b+c) vec A B`

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec G C is equal to a. vec0 b. 3 vec G A c. 3 vec G B d. 3 vec G C

( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= a. [ vec a\ vec b\ vec c] b. 0 c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

If vec a is parallel to vec bxx vec c , then ( vec axx vec b) . ( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . vec b) d. none of these

The scalar vec Adot [( ( vec B+ vec C)xx( vec A+ vec B+ vec C))] equals a. 0 b. [ vec A vec B vec C]+[ vec B vec C vec A] c. [ vec A vec B vec C] d. none of these

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Value of [ vec axx vec b , vec axx vec c , vec d] is always equal to a. ( vec adot vec d)[ vec a vec b vec c] b. ( vec adot vec c)[ vec a vec b vec d] c. ( vec adot vec b)[ vec a vec b vec d] d. none of these

If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx vec c = vec cxxvec a .

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these