Vector perpendicular to the plane

In summary, the vector v=(-2,1,a) is perpendicular to the plane z=6x-3y+4 when a=4/3. The normal vector of the plane is (6,-3,-1) and the dot product of v and n must be equal to 0 for them to be perpendicular.
  • #1
xstetsonx
78
0
For what value of a is the vector v=(-2,1,a) perpendicular to the plane z=6x-3y+4?

i looked the book and my teacher's solution they are different so i just want to make sure i did this right...


Vector v is perpendicular to the plane if it is parallel to the plane’s normal vector. A vector which is normal (= perpendicular) to the plane is n=(6,-3, 4) Hence, v parallel n if their coordinates are proportional, i.e. −2/6=1/3=a/4, therefore a=4/3



can someone correct me if i am wrong?PLZ
 
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  • #2
You got one component of the normal vector wrong.
 
  • #3
how? z=6x-3y+4 don't u just take the coefficient and that is your normal vector?
 
  • #4
Do you see a 4z in your equation?
 
  • #5
aw crap so is it -1 then?
 
Last edited:
  • #6
since i have two vectors why can't i do Vector1 . Vector2=0?
since the dot product says a.b=0 is perpendicular to each other?
 

Related to Vector perpendicular to the plane

1. What is a vector perpendicular to a plane?

A vector perpendicular to a plane is a vector that is at a right angle to all points on the plane. This means that the vector is perpendicular to all lines that lie in the plane.

2. How do you find a vector that is perpendicular to a plane?

To find a vector that is perpendicular to a plane, you can use the cross product of two non-parallel vectors that lie in the plane. The resulting vector will be perpendicular to both of the original vectors and therefore, perpendicular to the plane as well.

3. What is the relationship between a perpendicular vector and the normal vector of a plane?

The normal vector of a plane is a vector that is perpendicular to the plane. Therefore, any vector that is perpendicular to the plane will also be parallel to the normal vector.

4. Can a vector be perpendicular to more than one plane?

Yes, a vector can be perpendicular to more than one plane. This can happen if the planes intersect at a right angle, or if the vector is perpendicular to the line of intersection between the planes.

5. How is the dot product related to a vector perpendicular to a plane?

The dot product of two vectors is equal to zero when the vectors are perpendicular to each other. Therefore, if a vector is perpendicular to a plane, its dot product with any vector in the plane will be equal to zero.

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