Answer the following as true or false:

i. and are collinear.

ii. Two collinear vectors are always equal in magnitude.

iii. Zero vector is unique.

iv. Two vectors having same magnitude are collinear.

v. Two collinear vectors having the same magnitude are equal.

i. and are collinear. (True)

Two or more vectors that lie on the same line or on a parallel line to this are called collinear vectors.

and are collinear.

ii. Two collinear vectors are always equal in magnitude. (False)

Two or more vectors that lie on the same line or on a parallel line to this are called collinear vectors. Two collinear vectors may point in either same or opposite direction. And they are not necessarily equal in magnitude they can be of different magnitude also.

iii. Zero vector is unique.(True)

There is only one zero - vector in a vector space. Hence zero vector is unique.

iv. Two vectors having same magnitude are collinear. (False)

It is not necessary for two vectors having the same magnitude to be parallel to the same line. Hence two vectors having same magnitude need not be collinear.

v. Two collinear vectors having the same magnitude are equal.(False)

Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.