TS EAMCET · Maths · Vector Algebra
Let \(A(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) and \(B(13 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})\) be two points on a line \(L\). \(C\) and \(D\) be the points on \(L\) on either side of \(A\) at distance of 9 and 6 units respectively and \(C\) lies between \(A\) and \(B\). Then position vectors of \(C\) and \(D\) are respectively
- A \(-3 \hat{i}+4 \hat{j}-7 \hat{k}, 7 \hat{i}-\hat{j}+3 \hat{k}\)
- B \(9 \hat{i}-2 \hat{j}+5 \hat{k}, 7 \hat{i}-\hat{j}+3 \hat{k}\)
- C \(-3 \hat{i}+4 \hat{j}-7 \hat{k},-\hat{i}+3 \hat{j}-5 \hat{k}\)
- D \(9 \hat{i}-2 \hat{j}+5 \hat{k},-\hat{i}+3 \hat{j}-5 \hat{k}\)
Answer & Solution
Correct Answer
(D) \(9 \hat{i}-2 \hat{j}+5 \hat{k},-\hat{i}+3 \hat{j}-5 \hat{k}\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}\text { Given, } A(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}) \text { and } B(13 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+9 \hat{\mathbf{k}}) \\ A B=\sqrt{10^2+5^2+10^2}=15\end{gathered}\)…
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