JEE Mains · Maths · STD 12 - 10. vector algebra
A vector \(\vec{a}\) is parallel to the line of intersection of the plane determined by the vectors \(\hat{i}, \hat{i}+\hat{j}\) and the plane determined by the vectors \(\hat{i}-\hat{j}, \hat{i}+\hat{k}\). The obtuse angle between \(\vec{a}\) and the vector \(\vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}\) is
- A \(\frac{3 \pi}{4}\)
- B \(\frac{2 \pi}{3}\)
- C \(\frac{4 \pi}{5}\)
- D \(\frac{5 \pi}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{3 \pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\vec{n}_{1}=\hat{ i } \times(\hat{ i }+\hat{ j })=\hat{ k }\) \(\overrightarrow{ n }_{2}=(\hat{ i }+\hat{ k }) \times(\hat{ i }-\hat{ j })\) \(=\hat{ i }+\hat{ j }-\hat{ k }\) Line of intersection along \(\overrightarrow{ n }_{1} \times \overrightarrow{ n }_{2}\)…
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