Question:medium
The angle between the lines $\vec{r}=(3+\alpha)\hat{i}+2(1+\alpha)\hat{j}+2(-2+\alpha)\hat{k}$ and $\vec{r}=(5+3\beta)\hat{i}+2(1+\beta)\hat{j}+6\beta\hat{k}$ , where $\alpha$ and $\beta$ are parameters, is
The angle between the lines $\vec{r}=(3+\alpha)\hat{i}+2(1+\alpha)\hat{j}+2(-2+\alpha)\hat{k}$ and $\vec{r}=(5+3\beta)\hat{i}+2(1+\beta)\hat{j}+6\beta\hat{k}$ , where $\alpha$ and $\beta$ are parameters, is
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Logic Tip: The coefficients of the parameters ($\alpha$ and $\beta$) represent the components of the direction vectors directly. Extracting them mentally saves writing out the fully separated vector equation.
Updated On: Apr 27, 2026
- $\cos^{-1}\left(\frac{17}{21}\right)$
- $\cos^{-1}\left(\frac{19}{12}\right)$
- $\cos^{-1}\left(\frac{9}{21}\right)$
- $2\cos^{-1}\left(\frac{19}{21}\right)$
- $\cos^{-1}\left(\frac{19}{21}\right)$
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The Correct Option is
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