TS EAMCET · Maths · Vector Algebra
Let \(\overrightarrow{O A}=\hat{i}-3 \hat{j}+\hat{k}, \overrightarrow{O B}=\hat{i}+3 \hat{j}-2 \hat{k}\) and \(\overrightarrow{O C}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) be the position vectors of three points \(A, B\) and \(C\). Let \(P\) be the point which divides \(A B\) in the ratio \(2: 1\). If \(1, m, n\) are the direction cosines of the vector \(\overrightarrow{P C}\), then \(1+3 m+2 n=\)
- A \(23 / 7\)
- B \(5\)
- C \(18 / 7\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \vec{r}=\frac{2(\overrightarrow{O B})+1(\overrightarrow{O A})}{2+1}=\frac{2 \hat{i}+6 \hat{j}-4 \hat{k}+\hat{i}-3 \hat{j}+\hat{k}}{3} \\ & =\hat{i}+\hat{j}-\hat{k} \\ & \overrightarrow{P C}=\overrightarrow{O C}-\vec{r}=(4 \hat{i}+3 \hat{j}+5…
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