If a and b are two collinear vectors, then which of the following are…

If \(\vec{a}\)  and \(\vec{b}\)  are two collinear vectors, then they are parallel.

Therefore we have: \(\vec{b}\) = λ\(\vec{a}\), for some scalar λ = ±1 then \(\vec{a}\)= ±\(\vec{b}\)

If \(\vec{a}\)=  a₁\(\hat{i}\) + a₂\(\hat{j}\)+ a₃\(\hat{j}\) and  \(\vec{b}\)=  b₁\(\hat{i}\) + b₂\(\hat{j}\)+ b₃\(\hat{j}\) then

\(\vec{b}\) = λ\(\vec{a}\)

⇒  (b₁\(\hat{i}\) + b₂\(\hat{j}\)+ b₃\(\hat{j}\))  = λ(a₁\(\hat{i}\) + a₂\(\hat{j}\)+ a₃\(\hat{j}\))

⇒  (b₁/a₁) = (b₂/a₂) = (b₃/a₃) =λ

Thus  the respective components of \(\vec{a}\) and \(\vec{b}\)  are proportional.

However, vectors \(\vec{a}\) and \(\vec{b}\)   have different directions. Hence, the given statement in option (4) is incorrect.