TS EAMCET · Maths · Vector Algebra
If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{a} \cdot \mathbf{b}=1\) and \(\mathbf{a} \times \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}\), then \(\mathbf{b}=\)
- A \(2 \hat{\mathbf{i}}\)
- B \(2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\)
- C \(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\)
- D \(\hat{\mathbf{i}}\)
Answer & Solution
Correct Answer
(D) \(\hat{\mathbf{i}}\)
Step-by-step Solution
Detailed explanation
Let vector \(\mathbf{b}=b_1 \hat{\mathbf{i}}+b_2 \hat{\mathbf{j}}+b_3 \hat{\mathbf{k}}\), then \(\mathbf{a} \cdot \mathbf{b}=b_1+b_2+b_3=1\) (given ) and…
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