The vector you found, 14i - 1j - 4k (or <14, -1, -4>) is normal to (perpendicular to) the plane you're trying to find.Punkyc7 said:Let P(0,-5,3) vector v=4j -k and vector w=i+2j+3k
Find an eqaution of the plane passing through P and parallel to both v and w
so i found the vector perpendicular to both v and w which is 14 -1 -4 but I am not sure to find a plane that parrallel to v and w
The equation of a plane passing through a point is represented as Ax + By + Cz = D, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant value. This equation is derived using the point-slope form of a line and the equation for a plane in 3D space.
To find the equation of a plane passing through a point, you will need the coordinates of the given point and the normal vector of the plane. The normal vector can be calculated by finding the cross product of two vectors in the plane. Then, plug in the values of the point and the normal vector into the general equation of a plane (Ax + By + Cz = D) and solve for D to get the specific equation of the plane passing through the given point.
Yes, a plane passing through a point can have multiple equations. This is because the equation of a plane is not unique and can be represented in different forms. However, all of these equations will still represent the same plane and contain the same point and normal vector.
Yes, the equation of a plane passing through a point can be graphed in 3D space. The point will be the origin of the plane, and the normal vector will determine the direction and orientation of the plane. The plane itself will be infinite in size and can be represented by a 2D grid in 3D space.
The equation of a plane passing through a point is used in real life for various applications, such as in engineering, architecture, and aviation. It is used to calculate the position and orientation of objects in 3D space, as well as for creating 3D models and designs. It is also used in navigation systems to determine the trajectory of objects, such as airplanes and satellites.