Question

Find the vector equation of a plane passing through a point having position vector 2i - j + k and perpendicular to the vector 4i + 2j - 3k.

Answer 1

Given: Position vector of the point - \(\vec a=2\hat i-\hat j+\hat k\)

Point is perpendicular to the vector \(\vec n=4i + 2\hat j-3\hat k\)

To find: the vector equation of a plane passing through a point We know that, vector equation of a plane passing through a point  \(\vec a\) and normal to  \(\vec n\)  is given by

\((\vec r-\vec a).\vec n=0\)....(i)

Substituting the values from given criteria, we get

by multiplying the two vectors using the formula

is the vector equation of a plane passing through the given point.