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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

  1. A \(\frac{1}{\sqrt{14}}(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
  2. B \(\frac{1}{\sqrt{26}}(-\hat{\mathrm{i}}-4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
  3. C \(\frac{1}{\sqrt{26}}(-3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+\hat{\mathrm{k}})\)
  4. D \(\frac{1}{\sqrt{22}}(3 \hat{i}-4 \hat{j}+3 \hat{k})\)
Verified Solution

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…