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Home  >>  CBSE XII  >>  Math  >>  Model Papers
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Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane \( \overrightarrow r.(\hat i + 2\hat j - 5\hat k)+9=0\)

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Toolbox:
  • Equation of a line passing through a point and $\perp$ to the given plane is given by
  • $\overrightarrow l=\overrightarrow r +\lambda\overrightarrow N,\lambda\in R$
Step 1:
The position vector $\overrightarrow r$ of the given point (1,2,3) is $\overrightarrow r=\hat i+2\hat j+3\hat k$
The direction ratios of the normal vector is $\overrightarrow N=\hat i+2\hat j-5\hat k$
Equation of a line passing through a point and $\perp$ to the given plane is given by $\overrightarrow l=\overrightarrow r+\lambda\overrightarrow N,\lambda\in R$
Step 2:
Substituting for $\overrightarrow r$ and $\overrightarrow N$
$\Rightarrow \overrightarrow l=(\hat i+2\hat j+3\hat k)+\lambda(\hat i+2\hat j-5\hat k)$
This is the required vector equation.
answered Oct 4, 2013 by sreemathi.v
 

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