TS EAMCET · Maths · Vector Algebra
\(\hat{i}-2 \hat{j}+\hat{k}, 2 \hat{i}+\hat{j}-\hat{k}, \hat{i}-\hat{j}-2 \hat{k}\) are the position vectors of the vertices \(A, B, C\) of a triangle \(A B C\) respectively. If \(D\) and \(E\) are the mid points of \(B C\) and \(C A\) respectively, then the unit vector along \(\overrightarrow{D E}\) is
- A \(\frac{1}{7}(3 \hat{i}-2 \hat{j}+6 \hat{k})\)
- B \(\frac{1}{\sqrt{14}}(-\hat{i}-3 \hat{j}+2 \hat{k})\)
- C \(\frac{1}{\sqrt{3}}(\hat{i}-\hat{j}-\hat{k})\)
- D \(\frac{1}{13}(12 \hat{i}+3 \hat{j}+4 \hat{k})\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{14}}(-\hat{i}-3 \hat{j}+2 \hat{k})\)
Step-by-step Solution
Detailed explanation
\(\vec{D} \equiv \frac{3 \hat{i}}{2}-\frac{3 \hat{k}}{2} ; \quad \vec{E} \equiv \hat{i}-\frac{3}{2} \hat{j}-\frac{\hat{k}}{2} ; \vec{D} \vec{E} \equiv \frac{-\hat{i}}{2}-\frac{3}{2} \hat{j}+\hat{k}\) Vector along \(\overrightarrow{D E}\) is \(-\hat{i}-3 \hat{j}+2 \hat{k}\) Unit…
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