Question

Consider a vector $\overrightarrow{\text{A}}=3\hat{i}-4\hat{j}+2\hat{k}$, another vector that is parallel to $\overrightarrow{\text{A}}$ is

• A. $6\hat{i}+8\hat{j}+4\hat{k}$
• B. $-6\hat{i}+8\hat{j}+4\hat{k}$
• C. $-6\hat{i}+8\hat{j}-4\hat{k}$
• D. $6\hat{i}-8\hat{j}-2\hat{k}$

Answer 1

The correct option is C $-6\hat{i}+8\hat{j}-4\hat{k}$

A.

Let $\overrightarrow{A}=3\hat{i}-4\hat{j}+2\hat{k}$ and $\overrightarrow{B}=6\hat{i}+8\hat{j}+4\hat{k}$

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel if and only if they are scalar multiples of one another. i.e $\overrightarrow{A}=k\overrightarrow{B}.$ $k$ is a constant not equal to zero.

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=6\hat{i}+8\hat{j}+4\hat{k}$

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=2(3\hat{i}+4\hat{j}+2\hat{k})$

Here, $\overrightarrow{A}$ and $\overrightarrow{B}$ are not parallel.

B.

Let $\overrightarrow{A}=3\hat{i}-4\hat{j}+2\hat{k}$ and $\overrightarrow{B}=-6\hat{i}+8\hat{j}+4\hat{k}$

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel if and only if they are scalar multiples of one another. i.e $\overrightarrow{A}=k\overrightarrow{B}.$ $k$ is a constant not equal to zero.

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=-6\hat{i}+8\hat{j}+4\hat{k}$

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=-2(3\hat{i}-4\hat{j}-2\hat{k})$

Here, $\overrightarrow{A}$ and $\overrightarrow{B}$ are not parallel.

C.

Let $\overrightarrow{A}=3\hat{i}-4\hat{j}+2\hat{k}$ and $\overrightarrow{B}=-6\hat{i}+8\hat{j}-4\hat{k}$

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel if and only if they are scalar multiples of one another. i.e $\overrightarrow{A}=k\overrightarrow{B}.$ $k$ is a constant not equal to zero.

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=-6\hat{i}+8\hat{j}-4\hat{k}$

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=-2(3\hat{i}-4\hat{j}+2\hat{k})$

Here, $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel.

D.

Let $\overrightarrow{A}=3\hat{i}-4\hat{j}+2\hat{k}$ and $\overrightarrow{B}=6\hat{i}-8\hat{j}-4\hat{k}$

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel if and only if they are scalar multiples of one another. i.e $\overrightarrow{A}=k\overrightarrow{B}.$ $k$ is a constant not equal to zero.

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=6\hat{i}-8\hat{j}-4\hat{k}$

$\Rightarrow$ $3\hat{i}-4\hat{j}+2\hat{k}$ $=2(3\hat{i}-4\hat{j}-2\hat{k})$

Here, $\overrightarrow{A}$ and $\overrightarrow{B}$ are not parallel.

$\therefore$ The correct answer is option C.