The normal vector to the plane is given by the cross product of the two vectors in the plane.

First, we can write the determinant in order to take the cross product of the two vectors:

where i, j, and k are the unit vectors corresponding to the x, y, and z direction respectively.

Next, we take the cross product. One can do this by multiplying across from the top left to the lower right, and continuing downward, and then subtracting the terms multiplied from top right to the bottom left:

The normal vector to the plane is given by the cross product of the two vectors in the plane.

First, we can write the determinant in order to take the cross product of the two vectors:

where i, j, and k are the unit vectors corresponding to the x, y, and z direction respectively.

Next, we take the cross product. One can do this by multiplying across from the top left to the lower right, and continuing downward, and then subtracting the terms multiplied from top right to the bottom left:

The normal vector to the plane is given by the cross product of two vectors in the plane.

First, we must write the determinant in order to take the cross product of the two vectors:

where i, j, and k are the unit vectors corresponding to the x, y, and z direction respectively.

Next, we take the cross product. One can do this by multiplying across from the top left to the lower right, and continuing downward, and then subtracting the terms multiplied from top right to the bottom left:

To determine the normal vector to the plane, we must take the cross product of the two vectors in the plane.

First, we must write the determinant in order to take the cross product of the two vectors:

where i, j, and k are the unit vectors corresponding to the x, y, and z direction respectively.

Next, we take the cross product. One can do this by multiplying across from the top left to the lower right, and continuing downward, and then subtracting the terms multiplied from top right to the bottom left:

To solve the problem, we use the fact that two parallel planes have the same normal vector. The equation of on of the planes is given, and from that we know its normal vector is , which is the normal vector of the plane in question

To find the normal vector to the plane containing vectors  and , we find the determinant of the 3x3 matrix 

Plugging in the vectors and solving, we get

To find the normal vector to the plane containing vectors  and , we find the determinant of the 3x3 matrix 

Plugging in the vectors and solving, we get

First, we must write the determinant in order to take the cross product of the two vectors:

where i, j, and k are the unit vectors corresponding to the x, y, and z direction respectively.

Next, we take the cross product. One can do this by multiplying across from the top left to the lower right, and continuing downward, and then subtracting the terms multiplied from top right to the bottom left:

The difference between zero and the zero vector is an important one, because the result of a cross product is always a vector (the dot product of two vectors gives a scalar). 

To find the normal vector to the plane containing vectors  and , we take the cross product of the two. 

To find the cross product between the vectors  and , we find the determinant of the 3x3 matrix  which follows the formula 

Applying to the vectors from the problem statement, we get

To find the normal vector to the plane containing vectors  and , we take the cross product of the two. 

To find the cross product between the vectors  and , we find the determinant of the 3x3 matrix  which follows the formula 

Applying to the vectors from the problem statement, we get