Define zero vector.

Define unit vector.

Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.

Define the Vector

Define unit vector, null vector and position vector .

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?

If vecAxxvecB=vecC , then choose the incorrect option : [ vecA and vecB are non zero vectors]

If veca, vecb are non zero vectors, then ((vecaxxvecb)xxveca).((vecbxxveca)xxvecb) equals

If a,b and c are three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a( lamda being some non-zero scalar), then a+2b+6c is equal to

For some non zero vector vecv , if the sum of vecv and the vector obtained from vecv by rotating it by an angle 2alpha equals to the vector obtained from vecv by rotating it by alpha then the value of alpha , is

Let veca,vecb,vecc be three non-zero vectors such that [vecavecbvecc]=|veca||vecb||vecc| then