CUET · MATHS · PYQ PAPER 2023
The angle between the pair of straight lines given by \(\vec{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})\) and \(\vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\) is :
- A \(\cos ^{-1}\left(\frac{19}{21}\right)\)
- B \(\cos ^{-1}\left(\frac{17}{21}\right)\)
- C \(\quad \cos ^{-1}\left(\frac{11}{21}\right)\)
- D \(\cos ^{-1}\left(\frac{7}{21}\right)\)
Answer & Solution
Correct Answer
(A) \(\cos ^{-1}\left(\frac{19}{21}\right)\)
Step-by-step Solution
Detailed explanation
\(\vec{b_1} = \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b_2} = 3 \hat{i}+2 \hat{j}+6 \hat{k}\) \(\vec{b_1} \cdot \vec{b_2} = (1)(3) + (2)(2) + (2)(6) = 3+4+12 = 19\) \(|\vec{b_1}| = \sqrt{1^2+2^2+2^2} = \sqrt{9} = 3\) \(|\vec{b_2}| = \sqrt{3^2+2^2+6^2} = \sqrt{49} = 7\)…
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