Practicing Success
If \(\vec{a}\) and \(\vec{b}\) are two collinear vectors, then which of the following are incorrect- |
\(\vec{b}\)= λ\(\vec{a}\), for some scalar λ \(\vec{a}\)= ±\(\vec{b}\) the respective components of \(\vec{a}\) and \(\vec{b}\) are proportional both the components \(\vec{a}\) and \(\vec{b}\) have same direction, but different magnitude. |
both the components \(\vec{a}\) and \(\vec{b}\) have same direction, but different magnitude. |
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.
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