CUET · MATHS · PYQ PAPER 2025
Let \(L_1\) and \(L_2\) be two lines, represented as,
\(L_1: \vec{r}=\hat{i}+\hat{j}+\lambda(2 \hat{i}-\hat{j}+\hat{k})\) and \(L_2: \vec{r}=2 \hat{i}+\hat{j}-\hat{k}+\mu(4 \hat{i}-2 \hat{j}+2 \hat{k})\), where \(\lambda\) and \(\mu\) are scalars. Then which of the following are true?
(A)\(L_1\) is perpendicular to \(L_2\)
(B) \(L_1\) is parallel to \(L_2\)
(C) \(L_1\) passes through the point (1,1,0)
(D) \(L_2\) passes through the point (2,1,-1)
Choose the correct answer from the options given below:
- A (A) and (D) only
- B (B), (C) and (D) only
- C (C) and (D) only
- D (A) and (C) only
Answer & Solution
Correct Answer
(B) (B), (C) and (D) only
Step-by-step Solution
Detailed explanation
\((2 \hat{i}-\hat{j}+\hat{k}) \cdot (4 \hat{i}-2 \hat{j}+2 \hat{k}) = (2)(4)+(-1)(-2)+(1)(2) = 8+2+2 = 12 \neq 0 \Rightarrow\) (A) is false. \(4 \hat{i}-2 \hat{j}+2 \hat{k} = 2(2 \hat{i}-\hat{j}+\hat{k}) \Rightarrow\) (B) is true. \(L_1\) passes through…
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