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If the vector $P = (1,2,-1)$ is parallel to the plane $7x+2y+kz = 5$, then what's the value of $k$?
Deveno said:Do you know how to find the general formula for points parallel to a plane?
A vector is considered parallel to a plane when it lies entirely within the plane or is perpendicular to the plane's normal vector.
To determine if a vector is parallel to a plane, you can use the dot product. If the dot product between the vector and the plane's normal vector is equal to 0, then the vector is parallel to the plane.
Yes, a vector can be parallel to multiple planes. This occurs when the vector is perpendicular to the normal vectors of each plane.
To find the equation of a plane that is parallel to a given vector, you can use the point-normal form of a plane. This involves selecting a point on the plane and using the vector as the normal vector in the equation.
Yes, it is possible for a vector to be parallel to a plane but not lie in the same plane. This can occur when the vector is perpendicular to the plane's normal vector but does not intersect the plane at any point.