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`

If G be the centroid of the triangle ABC, then prove that vec(GA)+vec(GB)+vec(GC)=vec(0).

' 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 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 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

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

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

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= a. 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

ABCDE is a pentagon. Prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

A vector vec d is equally inclined to three vectors vec a= hat i+ hat j+ hat k , vec b=2 hat i+ hat ja n d vec c=3 hat j-2 hat kdot Let vec x , vec y ,a n d vec z be three vectors in the plane of vec a , vec b ; vec b , vec c ; vec c , vec a , respectively. Then a. vec x. vec d=-1 b. vec y. vec d=1 c. vec z. vec d=0 d. vec r. vec d=0,w h e r e vec r=lambda vec x+mu vec y+delta vec z