Question

Assertion :$\overrightarrow{a}=3\overrightarrow{i}+p\overrightarrow{j}+3\overrightarrow{k}$ and $\overrightarrow{b}=2\overrightarrow{i}+3\overrightarrow{j}+q\overrightarrow{k}$ are parallel vectors if $p=\frac{9}{2}$ and $q=2$. Reason: If $\overrightarrow{a}=a_1\overrightarrow{i}+a_2\overrightarrow{j}+a_3\overrightarrow{k}$ and $\overrightarrow{b}=b_1\overrightarrow{i}+b_2\overrightarrow{j}+b_3\overrightarrow{k}$ are parallel, then $\frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $\overrightarrow{a}=a_1\overrightarrow{i}+a_2\overrightarrow{j}+a_3\overrightarrow{k}$ and $\overrightarrow{b}=b_1\overrightarrow{i}+b_2\overrightarrow{j}+b_3\overrightarrow{k}$

Two vectors are said to be parallel if $\overrightarrow{a}=n.\overrightarrow{b}$

$\Rightarrow a_1=n{b}_1,a_2=n{b}_2,a_3=n{b}_3$

$\Rightarrow \frac{a_1}{b_1}=\frac{a_2}{b_2}=\frac{a_3}{b_3}$

$3=2\times n,p=3\times n,3=n\times q$

So $p=9/2,q=2$

Reason is the correct explanation for assertion.