If `vec(a) = vec(0) or vec(b) = vec(0) ` then `vec(a).vec(b) = 0 , ` show by an example that the converse of this statement is not always true .

If vec(a)=vec(OA) " and " vec(b)=vec(AB), " then " vec(a)+vec(b) is -

If vec(a) + vec(b) + vec (c ) = vec(0) , show that vec(a) xx vec(b) = vec(b) xx vec(c ) = vec(c ) xx vec(a)

If vec (a) + vec(b) + vec (c ) = vec(0) and |vec(a)| = 6 , |vec (b)| = 4 and |vec(c )| = 3 find the cosine of the angle between the vectors vec(b) and vec(c )

If either veca=vec0orvecb=vec0 , then vecaxxvecb=vec0 . Is the converse true ? Justify your answer with an example.

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

If vec(a),vec(b),vec (c ) are non - coplanar vectors vec (r) . vec(a) = vecr . vec(b) = vecr.vec(c ) = 0 , show that vec (r ) is a zero vector .

Given that vec(a) . vec(b) = 0 and vec(a) xx vec(b) = vec(0) . What can you conclude abut the vector vec(a) and vec(b) ?

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

If vec(a) + vec (b)+vec(c ) = vec (0) and |vec(a)| = 3 , |vec(b)| = 5 and |vec(c)| = 7 , , find the angle between the vectors vec(a) and vec(b)

If vec (a) xx vec(b) = vec (c ) xx vec(d) and vec (a) xx vec ( c) = vec (b) xx vec (d ) , show that vec(a) - vec (d) is parallel vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )