Question

$P(x_1,y_1)$ and $Q(x_2,y_2)$ are two points on the curve. $y=x^2+3x+1$. If $\overrightarrow{OP}.\hat{i}=1,\overrightarrow{OQ}.\hat{i}=-1$ then $|2\overrightarrow{OP}+3\overrightarrow{OQ}|$

• A. $2\sqrt{5}$
• B. $5\sqrt{2}$
• C. $8$
• D. $11$

Answer 1

The correct option is B $5\sqrt{2}$

$P=(x_1,y_1)$

$Q=(x_2,y_2)$

$\overline{OP}\cdot \overline{i}=1$

$\overline{OQ}\cdot \overline{i}=-1$

$x_1=1$

$x_2=-1$

$\overline{OP}=\overrightarrow{i}+5\overrightarrow{j}$

$\overline{OQ}=-\overrightarrow{i}-\overrightarrow{j}$

$|2\overrightarrow{OP}+3\overrightarrow{OQ}|=|(-\overrightarrow{i}+7\overrightarrow{j})|$

$=\sqrt{7^2+1}$

$=5\sqrt{2}$