AP EAMCET · Maths · Three Dimensional Geometry
The position vectors of \(A\) and \(B\) are \((\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\left.\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\right)\). If \(B\) divides the line \(A C\) in the ratio \(2: 1\), then position vector \(C\) is
- A \(\left(\frac{1}{2}, 0,0\right)\)
- B \(\left(0, \frac{1}{3}, 0\right)\)
- C \(\left(\frac{-1}{2}, \frac{-1}{2}, 0\right)\)
- D \(\left(\frac{-1}{2}, 0,0\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{-1}{2}, 0,0\right)\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{O A}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\mathbf{O B}=\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\) Given ratio = 2 : 1 Let m: n = 2:1 m = 2and n = 1…
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