Question

Three vectors are given as $P=3\hat{i}-4\hat{j},Q=6\hat{i}-8\hat{j}$ and $R=(3/4)\hat{i}-\hat{j}$, then which of the following is correct?

• A. $P,Q$ and $R$ are equal vectors
• B. $P$ and $Q$ are parallel but $R$ is not parallel
• C. $P,Q$ and $R$ are parallel
• D. None of the above

Answer 1

Answer: (C)

Given, $P=3\hat{i}-4\hat{j}$
and $Q=6\hat{i}-8\hat{j}=2(3\hat{i}-4\hat{j})=2P$
Also, $R=\frac{3}{4}\hat{i}-\hat{j}=\frac{1}{4}(3\hat{i}-4\hat{j})=\frac{P}{4}$
So, $P,Q$ and $R$ are parallel with unequal magnitude. Thus, they are not equals vectors.