TS EAMCET · Maths · Vector Algebra
Let \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) be two vectors. Then the projection vector of \(\mathbf{b}\) on a vector perpendicular to \(\mathbf{a}\) is
- A \(-\frac{2}{3}(2 \hat{i}-\hat{j}-2 \hat{k})\)
- B \(\hat{i}+4 \hat{j}+\hat{k}\)
- C \(\frac{13}{3} \hat{i}+\frac{4}{3} \hat{j}-\frac{11}{3} \hat{k}\)
- D \(\frac{31}{9} \hat{i}-\frac{20}{9} \hat{j}-\frac{41}{9} \hat{k}\)
Answer & Solution
Correct Answer
(D) \(\frac{31}{9} \hat{i}-\frac{20}{9} \hat{j}-\frac{41}{9} \hat{k}\)
Step-by-step Solution
Detailed explanation
Given, \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}\) The projection of vector \(\mathbf{b}\) on a vector…
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