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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 2 · Q25
Find the angle between the following two lines: r =2 i -5 j + k +λ(3 i +2 j +6 k ); r =7 i -6 k +μ( i +2 j +2 k )
Find the angle between the following two lines: \[\begin{aligned} & \vec{r}=2 \hat{i}-5 \hat{j}+\hat{k}+\lambda(3 \hat{i}+2 \hat{j}+6 \hat{k}) \\ & \vec{r}=7 \hat{i}-6 \hat{k}+\mu(\hat{i}+2 \hat{j}+2 \hat{k}) \end{aligned} \]
Marking-scheme solution
Let $\displaystyle \theta$ be the angle between the given lines. Then
$$\cos \theta=\left|\frac{(3 i+2 j+6 k) \cdot(i+2 j+2 k)}{\sqrt{9+4+36} \sqrt{1+4+4}}\right|=\frac{19}{21}
$$
$\displaystyle \boldsymbol{\operatorname { m }} \boldsymbol{\theta}=\boldsymbol{\operatorname { c o s }}^{\mathbf{- 1}}\left(\frac{19}{21}\right)$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.