JEE Mains · Maths · STD 11 - 9. straight line
Let A and B be two distinct points on the line \(\mathrm{L}: \frac{\mathrm{x}-6}{3}=\frac{\mathrm{y}-7}{2}=\frac{\mathrm{z}-7}{-2}\). Both A and B are at a distance \(2 \sqrt{17}\) from the foot of perpendicular drawn from the point \((1,2,3)\) on the line L . If O is the origin, then \(\overrightarrow{O A} \cdot \overrightarrow{O B}\) is equal to:
- A 49
- B 47
- C 21
- D 62
Answer & Solution
Correct Answer
(B) 47
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \overrightarrow{\mathrm{PQ}} \cdot \overrightarrow{\mathrm{~b}}=0 \\ & \Rightarrow 3(3 \lambda+5)+2(2 \lambda+5)-2(-2 \lambda+4) \\ & \Rightarrow 17 \lambda=-17 \Rightarrow \lambda=-1 \\ & \mathrm{Q}(3,5,9) \end{aligned}\) Let A \((3 \mu+6,2 \mu+7,-2 \mu+7)\)…
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