Question

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.

Answer 1

(i)

When two or more vectors are parallel to a same line, then these vectors are collinear.

Here, a → and − a → are parallel. So, a → and d → are collinear.

Thus, the given statement is true.

(ii)

When two or more vectors are parallel to same line, then these vectors are collinear.

Thus, the given statement is false.

(iii)

When two or more vectors are parallel to same line, then these vectors are collinear, they can have opposite direction. But, equal vectors must have same magnitude and direction.

Thus, the given statement is false.

(iv)

When two vectors have same magnitude and direction except their initial position points, then they are equal.

Thus, the given statement is false.