COMEDK · Maths · 33. Vector Algebra
If \(\theta\) be the angle between the vectors \(a=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(b=6 \hat{i}-3 \hat{j}+2 \hat{k}\), then
- A \(\cos \theta=\dfrac{4}{21}\)
- B \(\cos \theta=\dfrac{3}{19}\)
- C \(\cos \theta=\dfrac{2}{19}\)
- D \(\cos \theta=\dfrac{5}{21}\)
Answer & Solution
Correct Answer
(A) \(\cos \theta=\dfrac{4}{21}\)
Step-by-step Solution
Detailed explanation
The angle \(\theta\) between two vectors \(\vec{a}\) and \(\vec{b}\) is given by the formula \(\cos \theta = \dfrac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|}\). Given \(\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}\) and \(\vec{b} = 6\hat{i} - 3\hat{j} + 2\hat{k}\). Calculate the…
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