# Plane defined by two vectors

Two vectors on a plane are given as $a= 3i+5j$ and $b=4i+ 10j$. Find the vector that defines the plane.

I know I should find the normal vector by taking the cross product of the given two vectors which is $a \times b = 10k$ however I do not know how to infer from this the vector that defines the plane.

• A plane is defined by the vector normal to it, which is $10\hat k$ here May 21, 2017 at 14:10
• @Shreyas Why is it so? Could you please provide link to similar examples / related topics please? Most of the sources I found explains it using points and then defines a position vector and finds the plane. May 21, 2017 at 14:16
• how I look at it is that a line is defined by its direction vector. but a plane contains infinitely many lines on it so we cant define a direction on the surface of the plane. The only way to uniquely define a direction vector for a plane is by considering the one perpendicular to its surface. Hence the normal vector distinctly defines the direction of a plane. May 21, 2017 at 14:30