TS EAMCET · Maths · Vector Algebra
\(2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}-3 \hat{k}\) are the position vectors of two points \(A\) and \(B\) respectively and \(C\) divides \(A B\) in the ratio \(3: 2\). If \(3 \hat{i}-\hat{j}+2 \hat{k}\) is the position vector of a point \(D\), then the unit vector in the direction of \(\overrightarrow{C D}\) is
- A \(\frac{1}{7 \sqrt{2}}(8 \hat{i}-5 \hat{j}-3 \hat{k})\)
- B \(\frac{1}{\sqrt{266}}(4 \hat{i}-13 \hat{j}+9 \hat{k})\)
- C \(\frac{1}{3 \sqrt{42}}(8 \hat{i}-5 \hat{j}+17 \hat{k})\)
- D \(\frac{1}{7 \sqrt{2}}(8 \hat{i}-5 \hat{j}+3 \hat{k})\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{3 \sqrt{42}}(8 \hat{i}-5 \hat{j}+17 \hat{k})\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Position vector of } \vec{C}=\frac{7}{5} \hat{i}+0 \hat{j}-\frac{7}{5} \hat{k} \\ & \overrightarrow{C D}=(3 \hat{i}-\hat{j}+2 \hat{k})-\left(\frac{7}{5} \hat{i}+0 \hat{j}-\frac{7}{5} \hat{k}\right) \\ & =\frac{8}{5} \hat{i}-\hat{j}+\frac{17}{5}…
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