Find the second and third components of a vector n

Question

Find the second and third components of a vector n normal to the plane with the equation 12x+13y-14z=5 if the first component of the vector n is equal to 12.

The second component of n = ?

The third component of n = ?

Answer 1

The normal vector to the plane ax+by+cz=m is the vector <a,b,c> where a , b , c, m are constants.

You have all you need for the components.

Answer 2

Since n = <12,13,-14> is the correct direction and the 1st component is forced to be 12, this is the normal vector desired with the components listed. If the question does specify that the first component is 2, instead of 12, then I agree with Yesim's analysis.

Answer 3

Plane 12x + 13y - 14z = 5. Normal vector for this plane N = <12, 13, - 14>. So, vector n = <2, b, c> = kN =

<12k, 13k, - 14k>;

So, 2 = 12k, k = 1/6 and b = 13k = 13/6, c = -14k = - 14/6 = - 7/3.

n = <2, 13/6, - 7/3>