Q. 11

# Find the vector equation of the line passing through the point with position vector and perpendicular to the plane

Answer :

**Given -** and the vector has position vector

**To find –** The vector equation of the line passing through (1, - 2, 5) and perpendicular to the given plane

**Tip –** The equation of a plane can be given by where is the normal of the plane

A line parallel to the given plane will be in the direction of the normal and will have the direction ratios same as that of the normal.

**Formula to be used –** If a line passes through the point (a, b, c) and has the direction ratios as (a’, b’, c’), then its vector equation is given by where λ is any scalar constant

The required equation will be **for some scalar λ**

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Find the vector and Cartesian equations of the line through the point (1, 2, -4) and perpendicular to the two lines.

and

Mathematics - Board PapersWrite the vector equations of the following lines and hence determine the distance between them:

Mathematics - Board Papers