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otterandseal1
- 16
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- Homework Statement
- I'm struggling to get part b. I got part a to be (1,4,-1). Just got no clue for b. Pls help
- Relevant Equations
- Dont know what to put here
Can you find a normal to ##\pi_1##? You should be able to do this by inspection from its equation. Also, if two vectors are perpendicular, their dot product is 0.otterandseal1 said:Homework Statement:: I'm struggling to get part b. I got part a to be (1,4,-1). Just got no clue for b. Pls help
Relevant Equations:: Dont know what to put here
View attachment 259080
Is the normal (2,-1,-3)?Mark44 said:Can you find a normal to ##\pi_1##? You should be able to do this by inspection from its equation. Also, if two vectors are perpendicular, their dot product is 0.
Yes.otterandseal1 said:Is the normal (2,-1,-3)?
is that using r.n = a.n ?ehild said:Yes.
You can find the normal of the other plane if you know two vectors the plane contains.
If ##\vec a## and ##\vec b## are vectors that lie in the plane you're trying to find the equation of, then ##\vec a \times \vec b## gives you a normal to that plane.otterandseal1 said:is that using r.n = a.n ?
Could you possibly show me the working for the question please?Mark44 said:If ##\vec a## and ##\vec b## are vectors that lie in the plane you're trying to find the equation of, then ##\vec a \times \vec b## gives you a normal to that plane.
No, can't do that, per the forum rules. See https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/, under Homework Guidelines.otterandseal1 said:Could you possibly show me the working for the question please?
Could I use the vector from part a? and the normal of the first plane?Mark44 said:No, can't do that, per the forum rules. See https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/, under Homework Guidelines.
Can you find two vectors in the plane you're trying to find?
If so, can you find their cross product? That will give you a normal to that plane. Once you have the normal, all you need is a single point in the plane, and you can find its equation.
What vector do you mean? And, yes. as the two planes are perpendicular the second plane contains the normal of the first plane.otterandseal1 said:Could I use the vector from part a? and the normal of the first plane?
Where the line meets the first planeehild said:What vector do you mean? And, yes. as the two planes are perpendicular the second plane contains the normal of the first plane.
No, it is a point , common point of the first plane an the line I. P (1,4,-1) is the position vector a of this point, it does not lie in the plane as vector b. But the line I lies in the second plane and so is its direction vector. What is it?otterandseal1 said:Where the line meets the first plane
Vectors are mathematical objects that have both magnitude and direction, and are often represented as arrows. Planes are flat surfaces that extend infinitely in all directions.
Vectors can be used to define planes by specifying a point on the plane and a direction perpendicular to it. This is known as the normal vector of the plane.
Some common operations involving vectors and planes include finding the angle between two vectors, projecting a vector onto a plane, and finding the intersection of two planes.
To determine if a point lies on a plane, you can substitute the coordinates of the point into the equation of the plane. If the resulting equation is true, then the point lies on the plane.
The equation of a plane in three-dimensional space is Ax + By + Cz = D, where A, B, and C are the coefficients of the variables x, y, and z, and D is a constant. This equation is known as the standard form of a plane.