AP EAMCET · Maths · Vector Algebra
\(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=\overrightarrow{\mathbf{a}} \cdot(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})=\overrightarrow{\mathbf{a}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}})=1\), then \(\overrightarrow{\mathbf{a}}\) is equal to :
- A \(\hat{\mathbf{i}}-\hat{\mathbf{k}}\)
- B \(1 / 3(3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
- C \(1 / 3(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
- D \(1 / 3(3 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Answer & Solution
Correct Answer
(D) \(1 / 3(3 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Step-by-step Solution
Detailed explanation
Let \(\overrightarrow{\mathbf{a}}=a_1 \hat{\mathbf{i}}+a_2 \hat{\mathbf{j}}+a_3 \hat{\mathbf{k}}\) \(\because \quad \overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=1\)…
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