# Find the vector, and Cartesian equations of a plane which passes through the point (1, 4, 6) and the normal vector to the plane is Given :

A = (1, 4, 6) To Find : Equation of plane.

Formulae :

1) Position Vector :

If A is a point having co-ordinates (a1, a2, a3), then its position vector is given by, 2) Dot Product :

If are two vectors  then, 3) Equation of plane :

Equation of plane passing through point A and having as a unit vector normal to it is Where, Position vector of point A = (1, 4, 6) is Now, = (1×1) + (4×(-2)) + (6×1)

= 1 – 8 + 6

= - 1

Equation of plane is  This is vector equation of the plane.

As Therefore = (x × 1) + (y × (-2)) + (z × 1)

= x - 2y + z

Therefore equation of the plane is This is Cartesian equation of the plane.

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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers