Can you have `vecAxxvecB=vecA.vecB` with A!=0 and B!=0?` What if one of the two vectors is zero?

Assertion : The direction of a zero (null) vector is indeteminate. Reason : We can have vecAxx vecB = vecA *vecB with vecA ne vec0 and vecB ne vec0 .

If veca*veca=0andveca*vecab=0 , then what can be concluded about the vector vecb ?

There are two vectors vecA=3hati+hatj and vecB=hatj+2hatk . For these two vectors- (a) Find the component of vecA along vecB in vector form. (b) If vecA & vecB are the adjacent sides of a parallalogram then find the magnitude of its area. (c) Find a unit vector which is perpendicular to both vecA & vecB .

Two vectors vecA and vecB are such that vecA+vecB=vecC and A^(2)+B^(2)=C^(2) . Which of the following statements, is correct:-

If vecA+ vecB = vecC and A+B+C=0 , then the angle between vecA and vecB is :

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

If |vecAxxvecB|=AB , then angle between vecA and vecB will be zero.

Two vectors vecA and vecB lie in a plane, another vector vecC lies outside this plane, then the resultant of these three vectors i.e. vecA+vecB+vecC

If vecA.vecB=vec0 and vecAxxvecC=vec0 , then the angle between vecB and vecC is

Answer the following : (i) A vector has magnitude & direction. Does it have a fixed location in space? Can it vary with time. (ii) Will two equal vectors vec(a) & vec(b) at different locations in space necessarily have identical physical effects? (iii) Can three non zero vectors, not in one plane, give a zero resulatnt? Can four vectors do ? (iv) Can a vector have zero magnitude if one of its components is not zero?