AP EAMCET · Maths · Vector Algebra
If the position vectors of the points \(A\) and \(B\) are \(2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}-\hat{j}+2 \hat{k}\) respectively, then the unit vector along \(\overrightarrow{\mathrm{BA}}\) and in the direction of \(\overrightarrow{\mathrm{AB}}\) is
- A \(\frac{1}{\sqrt{14}}(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
- B \(\frac{1}{\sqrt{26}}(-\hat{\mathrm{i}}-4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
- C \(\frac{1}{\sqrt{26}}(-3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
- D \(\frac{1}{\sqrt{22}}(3 \hat{i}-4 \hat{j}+3 \hat{k})\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{\sqrt{26}}(-\hat{\mathrm{i}}-4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
Step-by-step Solution
Detailed explanation
\(\overrightarrow{\mathrm{AB}}=-\hat{i}-4 \hat{j}+3 \hat{k}\) So, \(\overrightarrow{\mathrm{BA}}=\hat{i}-4 \hat{j}+3 \hat{k}\) Unit vector along \(\overrightarrow{\mathrm{BA}}\) and in direction \(\overrightarrow{\mathrm{AB}}\) is…
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