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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 66 of 78
Marks: +1, -0
Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane r⃗⋅(i^+2j^−5k^)+9=0.\vec{r} \cdot (\hat{i}+\hat{2j}-\hat{5k})+9=0 .
Solution:  
The given plane is r⃗⋅(i^+2j^−5k^)+9=0\vec{r} \cdot (\hat{i}+\hat{2j}-\hat{5k})+9=0...(1)
∴The direction ratios of the normal to the plane (1) are <1, 2, –5 >
∴ The equation of the required line is r⃗=(i^+2j^+3k^)\vec{r}=(\hat{i}+\hat{2j}+\hat{3k}) +λ(i^+2j^−5k^)+\lambda (\hat{i}+\hat{2j}-\hat{5k})
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