Is the vector parallel to the plane?

In summary, a vector is a mathematical quantity that represents a magnitude and direction in space. A plane is a two-dimensional flat surface that extends infinitely in all directions. To determine if a vector is parallel to a plane, you can use the dot product. A normal vector is a vector that is perpendicular to a plane and can be found by taking the cross product of two non-parallel vectors on the plane. To find the normal vector of a plane, you can use the formula n = (a, b, c) or find two non-parallel vectors and take their cross product.
  • #1
mathmari
Gold Member
MHB
5,049
7
Hello! :eek:

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)
 
Physics news on Phys.org
  • #2
mathmari said:
Hello! :eek:

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)

Yes
 
  • #3
Prove It said:
Yes

Ok... Thank you! (Smile)
 

FAQ: Is the vector parallel to the plane?

What is a vector?

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.

What is a plane?

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.

How do I determine if a vector is parallel to a plane?

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.

What is a normal vector?

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.

How do I find the normal vector of a 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.

Similar threads

MHB Distance between two non parallel lines
Replies
2
Views
7K
MHB Plane that is constructed by vectors
Replies
3
Views
1K
MHB Find Equation of Line Passing Through $(1, -2, -3)$ & Perpendicular to Plane
Replies
2
Views
2K
MHB Three vectors are on the same plane
Replies
2
Views
2K
MHB Volume of Liquid: Proving $\overrightarrow{v}\cdot\overrightarrow{n}$
Replies
2
Views
2K
MHB Spherical coordinates - Orthonormal system
Replies
7
Views
2K
MHB Cylindrical coordinates - Orthonormal system
Replies
5
Views
2K
MHB Find the Intersection Point of Lines $(3,1,-2)$ and $x=-1+t, y=-2+t, z=-1+t$
Replies
2
Views
1K
MHB Using vector notation describe a triangle
Replies
7
Views
2K
MHB Work of the vector field-Stokes' Theorem
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top