mathmari said:Hello!
When a plane contains the line $\overrightarrow{v}_1=\overrightarrow{a}+t\overrightarrow{u}$, does this mean that the vector $\overrightarrow{u}$ is parallel to the plane?? (Wondering)
Prove It said:
A vector is a mathematical quantity that represents a magnitude and direction in space. It can be represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.
A plane is a two-dimensional flat surface that extends infinitely in all directions. It can be represented by a flat sheet of paper or a geometric shape with four sides.
To determine if a vector is parallel to a plane, you can use the dot product. If the dot product of the vector and the normal vector of the plane is equal to zero, then the vector is parallel to the plane.
A normal vector is a vector that is perpendicular to a plane. It is often represented by the letter "n" and can be found by taking the cross product of two non-parallel vectors that lie on the plane.
To find the normal vector of a plane, you can use the formula n = (a, b, c), where a, b, and c are the coefficients of the equation of the plane in the form ax + by + cz = d. Alternatively, you can find two non-parallel vectors on the plane and take their cross product to find the normal vector.