AP EAMCET · Maths · Vector Algebra
If \(\bar{a}=\bar{i}+\bar{j}, \bar{b}=2 \bar{j}-\bar{k}\) are two vectors such that \(\bar{r} \times \bar{a}=\bar{b} \times \bar{a}, \bar{r} \times \bar{b}=\bar{a} \times \bar{b}\), then the unit vector in the direction of \(\overline{\mathrm{r}}\) is
- A \(\frac{1}{\sqrt{11}}(\overline{\mathrm{i}}+3 \overline{\mathrm{j}}-\overline{\mathrm{k}})\)
- B \(\frac{1}{\sqrt{11}}(\overline{\mathrm{i}}-3 \overline{\mathrm{j}}+\overline{\mathrm{k}})\)
- C \(\frac{1}{\sqrt{3}}(\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}})\)
- D \(\frac{1}{\sqrt{3}}(\overline{\mathrm{i}}+\overline{\mathrm{j}}-\overline{\mathrm{k}})\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{11}}(\overline{\mathrm{i}}+3 \overline{\mathrm{j}}-\overline{\mathrm{k}})\)
Step-by-step Solution
Detailed explanation
\((\bar{r} - \bar{b}) \times \bar{a} = \bar{0} \implies \bar{r} = \bar{b} + k_1 \bar{a}\) \((\bar{r} - \bar{a}) \times \bar{b} = \bar{0} \implies \bar{r} = \bar{a} + k_2 \bar{b}\)…
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