MHT CET · Maths · Three Dimensional Geometry
The ratio in which the plane \(\bar{r}\). \((\hat{i}-2 \hat{j}+3 \hat{k})=17\) divides the line joining the points \(-2 \hat{i}+4 \hat{j}+7 \hat{k}\) and \(3 \hat{i}-5 \hat{j}+8 \hat{k}\)
- A 10:3
- B \(3: 10\)
- C \(5: 3\)
- D \(4: 5\)
Answer & Solution
Correct Answer
(B) \(3: 10\)
Step-by-step Solution
Detailed explanation
Let the required ratio be \(\lambda: 1\) then the point of division lies on the plane.
\(\begin{aligned} & \frac{3 \lambda-2}{\lambda+1}-2 x \frac{-5 \lambda+4}{\lambda+1}+3 \times \frac{8 \lambda+7}{\lambda+1}=17 \\ & \Rightarrow \lambda=\frac{3}{10}\end{aligned}\)
The required ratio is \(3: 10\)
\(\begin{aligned} & \frac{3 \lambda-2}{\lambda+1}-2 x \frac{-5 \lambda+4}{\lambda+1}+3 \times \frac{8 \lambda+7}{\lambda+1}=17 \\ & \Rightarrow \lambda=\frac{3}{10}\end{aligned}\)
The required ratio is \(3: 10\)
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