JEE Mains · Maths · STD 12 - 10. vector algebra
Let the point A divide the line segment joining the points \(P(-1,-1,2)\) and \(Q(5,5,10)\) internally in the ratio \(\mathrm{r}: 1(\mathrm{r}\gt0)\). If O is the origin and \((\overrightarrow{\mathrm{OQ}} \cdot \overrightarrow{\mathrm{OA}})-\frac{1}{5}|\overrightarrow{\mathrm{OP}} \times \overrightarrow{\mathrm{OA}}|^2=10\), then the value of r is :
- A \(\sqrt{7}\)
- B 14
- C 3
- D 7
Answer & Solution
Correct Answer
(D) 7
Step-by-step Solution
Detailed explanation
\begin{aligned} & A=\left(\frac{5 r-1}{r+1}, \frac{5 r-1}{r+1}, \frac{10 r+2}{r+1}\right) \\ & (\overrightarrow{O Q} \cdot \overrightarrow{O A})-\frac{1}{5}|\overrightarrow{O P} \times \overrightarrow{O A}|^2=10 \\ & \overrightarrow{O Q}=5 \hat{i}+5 \hat{j}+10 \hat{k} \\ &…
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