Search any question & find its solution
Question:
Answered & Verified by Expert
Let $\overrightarrow{\mathbf{u}}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \overrightarrow{\mathbf{v}}=2 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}, \overrightarrow{\mathbf{w}}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{p}}=\overrightarrow{\mathbf{u}}+\overrightarrow{\mathbf{v}}+\overrightarrow{\mathbf{w}}$.
Which one of the following is correct?
Options:
Which one of the following is correct?
Solution:
1403 Upvotes
Verified Answer
The correct answer is:
$3 \overrightarrow{\mathbf{u}}+2 \overrightarrow{\mathbf{v}}=\overrightarrow{\mathbf{p}}$
$$
\begin{aligned}
\text { Since, } \overrightarrow{\mathrm{p}}=\overrightarrow{\mathrm{u}}+\overrightarrow{\mathrm{v}}+\overrightarrow{\mathrm{w}} \\
\Rightarrow & \overrightarrow{\mathrm{p}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+(2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}})+(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}})=7 \hat{\mathrm{i}}+7 \hat{\mathrm{j}} \\
& \text { Now, } 3 \overrightarrow{\mathrm{u}}+2 \overrightarrow{\mathrm{v}}=3(\hat{\mathrm{i}}-\hat{\mathrm{j}})+2(2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}})=\\
& \hat{3}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}=7 \hat{\mathrm{i}}+7 \hat{\mathrm{j}} \\
\Rightarrow & 3 \overrightarrow{\mathrm{u}}+2 \overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{p}}
\end{aligned}
$$
\begin{aligned}
\text { Since, } \overrightarrow{\mathrm{p}}=\overrightarrow{\mathrm{u}}+\overrightarrow{\mathrm{v}}+\overrightarrow{\mathrm{w}} \\
\Rightarrow & \overrightarrow{\mathrm{p}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+(2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}})+(4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}})=7 \hat{\mathrm{i}}+7 \hat{\mathrm{j}} \\
& \text { Now, } 3 \overrightarrow{\mathrm{u}}+2 \overrightarrow{\mathrm{v}}=3(\hat{\mathrm{i}}-\hat{\mathrm{j}})+2(2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}})=\\
& \hat{3}-3 \hat{\mathrm{j}}+4 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}=7 \hat{\mathrm{i}}+7 \hat{\mathrm{j}} \\
\Rightarrow & 3 \overrightarrow{\mathrm{u}}+2 \overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{p}}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.