Give a condition that three vectors ` vec a , vec b` and ` vec c` from the three sides of a triangle. What are the other possibilities?

Prove that a necessary and sufficient condition for three vectors vec a , vec b and vec c to be coplanar is that there exist scalars l , m , n not all zero simultaneously such that l vec a+m vec b+n vec c= vec0dot

If vec a ,\ vec b ,\ vec c are position vectors of the vertices of a triangle, then write the position vector of its centroid.

Show that the vectors vec a , vec b and vec c are coplanar if vec a+ vec b , vec b+ vec c and vec c+ vec a are coplanar.

If three unit vectors vec a , vec b , and vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec a and vec bdot

If vec a ,\ vec b ,\ vec c\ represent the sides of a triangle taken in order, then write the value of vec a+ vec b+ vec c

Let vec a , vec b , vec c be three vectors such that | vec a|=1,| vec b|=2a n d| vec c|=3. If the projection of vec b along a is equal to the projection of vec c along vec aa n d vec b , vec c are perpendicular to each other, find |3 vec a-2 vec b+2 vec c|dot

If vec(A), vec(B) and vec(C ) are three vectors, then the wrong relation is :

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 vecd dot vec a= vecd dot vec b= vec d dot vec ca 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 O A B C is a tetrahedron where O is the orogin anf A ,B ,a n dC are the other three vertices with position vectors, vec a , vec b ,a n d vec c respectively, then prove that the centre of the sphere circumscribing the tetrahedron is given by position vector (a^2( vec bxx vec c)+b^2( vec cxx vec a)+c^2( vec axx vec b))/(2[ vec a vec b vec c]) .

If vec a,vec b,vec c are three vectors such that vec a=vec b+vec c and the angle between vec b and vec c is pi/2, then