TS EAMCET · Maths · Vector Algebra
If the vector \(\mathbf{a}=3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) is the sum of two vectors \(\mathbf{a}_1\) and \(\mathbf{a}_2\), vector \(\mathbf{a}_1\) is parallel to \(\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and vector \(\mathbf{a}_2\) is perpendicular to \(\mathbf{b}\), then \(\mathbf{a}_1=\)
- A \(\frac{1}{2}(\hat{\mathbf{i}}+\hat{\mathbf{j}})\)
- B \(\frac{1}{3}(\hat{\mathbf{i}}+\hat{\mathbf{j}})\)
- C \(\frac{2}{3}(\hat{i}+\hat{\mathbf{j}})\)
- D \(\frac{3}{2}(\hat{\mathbf{i}}+\hat{\mathbf{j}})\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2}(\hat{\mathbf{i}}+\hat{\mathbf{j}})\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{aligned} & \mathbf{a}=3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} \text { and } \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}} \\ & \mathbf{a}=\mathbf{a}_1+\mathbf{a}_2 \end{aligned}\)…
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