AP EAMCET · Maths · Vector Algebra
Let \((\vec{a}, \vec{b})\) denote the angle between vectors \(\vec{a}\) and \(\vec{b}\). If \(\vec{a}=2 \hat{i}+3 \hat{j}+6 \hat{k}, \vec{a} \cdot \vec{b}=4\) and \((\vec{a}, \vec{b})=\cos ^{-1}\left(\frac{4}{21}\right)\), then \(\overline{\mathrm{a}}+\overline{\mathrm{b}}=\)
- A \(3 \hat{i}+\hat{j}+8 \hat{k}\)
- B \(3 \hat{i}+5 \hat{j}+4 \hat{k}\)
- C \(3 \hat{i}+5 \hat{j}+8 \hat{k}\)
- D \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+8 \hat{\mathrm{k}}\)
Answer & Solution
Correct Answer
(D) \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+8 \hat{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \bar{a}=2 \hat{i}+3 \hat{j}+6 \hat{k} \Rightarrow|\bar{a}|=7 \\ & \bar{a} \cdot \bar{b}=4 \\ & \Rightarrow|\bar{a}| \cdot|\bar{b}| \cos \theta=4 \\ & \Rightarrow \quad 7 \cdot|\bar{b}| \times \frac{4}{21}=4 \\ & \Rightarrow \quad 7 \times|\bar{b}|…
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