TS EAMCET · Maths · Three Dimensional Geometry
Let \(A(3,2,-4)\) and \(B(9,8,-10)\) be two points. Let \(P_1\) divide \(A B\) in the ratio \(1: 2\) and \(P_2\) divide \(A B\) in the ratio \(2: 1\). If the point \(P(\alpha, \beta, \gamma)\) divides \(P_1 P_2\) in the ratio \(1: 1\), then \(\alpha+2 \beta+2 \gamma=\)
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Let \(A(3,2,-4)\) and \(B(9,8,-10)\) be two points \(P\), divide \(A B\) in \(1: 2\) So, coordinate of \[ \begin{aligned} & P_1\left(\frac{2 \times 3+9}{3}, \frac{2 \times 2+1 \times 8}{3}, \frac{2 \times(-4)+1(-10)}{3}\right) \\ & \Rightarrow P_1(5,4,-6) \end{aligned} \] Now,…
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