Answer the following as true or false.

(i) and are collinear.

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

(iii) Two vectors having same magnitude are collinear.

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

(i) and are collinear: True

Explanation: and are parallel vectors, so, they are collinear.

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

Explanation: we know, and are unit vectors, so they have same magnitude but and are vectors along x – axis and y – axis respectively.

(iii) Two vectors having same magnitude are collinear: False

Explanation: Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.

We know, and are unit vectors, so they have same magnitude but and are vectors along x – axis and y – axis respectively. Since, they are not parallel to each other, so, they are not collinear.

(iv) Two collinear vectors having the same magnitude are equal: False

Explanation: Two vector are said to be equal, if they have the same magnitude and direction.

and are collinear vectors as they are parallel to each other and also they have same magnitude. But they do not have same direction, so, they are unequal vectors.