Question

Which of the following pairs of vectors are parallel?

• A. $\overrightarrow{A}=\hat{i}-2\hat{j}$ ; $\overrightarrow{B}=\hat{i}-5\hat{j}$
• B. $\overrightarrow{A}=\hat{i}-10\hat{j}$ ; $\overrightarrow{B}=2\hat{i}-5\hat{j}$
• C. $\overrightarrow{A}=\hat{i}-5\hat{j}$ ;$\overrightarrow{B}=\hat{i}-10\hat{j}$
• D. $\overrightarrow{A}=\hat{i}-5\hat{j}$ ; $\overrightarrow{B}=2\hat{i}-10\hat{j}$

Answer 1

The correct option is D $\overrightarrow{A}=\hat{i}-5\hat{j}$ ; $\overrightarrow{B}=2\hat{i}-10\hat{j}$

Let $\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors

Both vector will be parallel if $\overrightarrow{A}\times \overrightarrow{B}=0$ i.e, the cross multiplication will be zero.

Cross multiplication of both vectors in each option:-

$\left(A\right)$

$\overrightarrow{A}\times \overrightarrow{B}=-3\hat{k}$

$\left(B\right)$

$\overrightarrow{A}\times \overrightarrow{B}=15\hat{k}$

$\left(C\right)$

$\overrightarrow{A}\times \overrightarrow{B}=-5\hat{k}$

$\left(D\right)$

$\overrightarrow{A}\times \overrightarrow{B}=0\hat{k}$

Since , in option $\left(D\right)$ the cross multiplication of vectos A and B is zero.

Hence, option $\left(D\right)$ is correct answer.