TS EAMCET · Maths · Vector Algebra
If \(\hat{i}+\hat{j}, \hat{j}+\hat{k}, \hat{k}+\hat{i}, \hat{i}-\hat{j}, \hat{j}-\hat{k}\) are the position vectors of the points \(A, B, \dot{C}, D, E\) respectively, then the point of intersection of the line \(A B\) and the plane passing through \(C, D, E\) is
- A \(\hat{i}+\hat{j}+\hat{k}\)
- B \(\frac{1}{2} \hat{i}+\hat{j}+\frac{1}{2} \hat{k}\)
- C \(\frac{1}{2}(\hat{i}+\hat{j}+\hat{k})\)
- D \(\frac{1}{2} \hat{i}-\hat{j}+\frac{1}{2} \hat{k}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2} \hat{i}+\hat{j}+\frac{1}{2} \hat{k}\)
Step-by-step Solution
Detailed explanation
Equation of line \(A B\) \(\begin{aligned} & \vec{r}=\hat{i}+\hat{j}+\lambda(-\hat{i}+\hat{k}) \\ & \Rightarrow \frac{x-1}{-1}=\frac{y-1}{0}=\frac{z-0}{1}=\lambda \\ & \Rightarrow x=-\lambda+1, y=\hat{1}, z=\lambda \end{aligned}\) Equation of plane passing through \(C, D\) and…
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