Subjective Type

Answer the following as true or false. (i) a⃗ and −a⃗ 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.

Solution

(i)
Two vectors are said to be be collinear vectors if they are parallel to the same line. In other words, any two parallel vectors are collinear.
Since, the negative of $$\vec{a}$$ i.e. $$-\vec{a}$$ is a vector having same magnitude but opposite direction.
So, $$\vec{a} , -\vec{a}$$ are collinear vectors.

(iii)
Given statement is "False".
As collinear vectors are those vectors that are parallel to the same line.

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