Question

If $\overrightarrow{A}=6\hat{i}+8\hat{j},\overrightarrow{B}=210\hat{i}+280\hat{k}$, $\overrightarrow{C}=5.1\hat{i}+6.8\hat{j},\overrightarrow{D}=3.6\hat{i}+8\hat{j}+48\hat{k}$,

then which of the given vectors are parallel?

• A. $\overrightarrow{A}$ and $\overrightarrow{B}$
• B. $\overrightarrow{A}$ and $\overrightarrow{C}$
• C. $\overrightarrow{A}$ and $\overrightarrow{D}$
• D. $\overrightarrow{C}$ and $\overrightarrow{D}$

Answer 1

Answer: (B)

$\overrightarrow{A}$ and $\overrightarrow{C}$

Given

$\overrightarrow{A}=6\hat{i}+8\hat{j}\overrightarrow{B}=210\hat{i}+280\hat{k}\overrightarrow{C}=5.1\hat{i}+6.8\hat{j}\overrightarrow{D}=3.6\hat{i}+8\hat{j}+48\hat{k}$

if $\overrightarrow{u}=\lambda \overrightarrow{u}$ the u is parallel So Comparing $\overrightarrow{A}and\overrightarrow{B}$

$6\hat{i}+8\hat{j}\ne \lambda (210\hat{i}+280\hat{k})$

So Comparing $\overrightarrow{A}and\overrightarrow{C}$

$6\hat{i}+8\hat{j}=\lambda (5.1\hat{i}+6.8\hat{j})$

So $\overrightarrow{A}and\overrightarrow{C}$ are parallel