00:01
In this question, where asked to find an equation of the plane through the point p and parallel to the plane z minus 3x plus 4y equals to negative 9.
00:11
And the formula for the plane is ax plus by plus cz plus d equals 0, where a, b, c and d are the coefficients to be found.
00:26
Now, recall that two planes are parallel if their normal vectors are parallel.
00:32
I recall that the normal vector of a plane is basically the coefficients of x, y and z in the equation of the plane.
00:43
So the normal vector of our plane, let the normal vector of our plane be equal to n2.
01:01
Normal vector of the plane of this plane here.
01:08
And 1 is a normal vector to the plane z.
01:19
Z and after distributing the negative sign over parentheses we are going to get minus 3x minus 4y equals to negative 9 or we can write it as negative 3x minus 4y plus z equals to negative 9 and as i told you before the coordinates of a normal vector are the coefficients in front of x, y and z in the equation of the plane and since we know this the equation of one plane, we can find the coordinates of the normal vector n1.
02:14
The coordinates of n1 are the coefficients in front of x, y and z, and are negative 3, negative 4, and 1...