COMEDK · Maths · 33. Vector Algebra
\(\text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is }\)
- A \(\dfrac{2 \pi}{3}\)
- B \(\dfrac{3 \pi}{4}\)
- C \(\dfrac{\pi}{3}\)
- D \(\dfrac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
Let \(\vec{a} = \hat{i} - \hat{j}\) and \(\vec{b} = \hat{j} - \hat{k}\). The dot product is given by \(\vec{a} \cdot \vec{b} = (1)(0) + (-1)(1) + (0)(-1) = -1\). The magnitudes are \(|\vec{a}| = \sqrt{1^2 + (-1)^2 + 0^2} = \sqrt{2}\) and…
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