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anonymous
 5 years ago
) The two vectors u<1,2,3> and v = <2,3,2> determine a plane in space. Mark each of the vectors below as "T" if the vector lies in the same plane as u and "F" if not.
anonymous
 5 years ago
) The two vectors u<1,2,3> and v = <2,3,2> determine a plane in space. Mark each of the vectors below as "T" if the vector lies in the same plane as u and "F" if not.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01. <3,0,0> 2. <6,9,6> 3. <4,7,8> 4. <3,4,1>

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There are a couple of ways I can think of to solve this, what do you think might be some useful properties to use?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0First i dont get what does that mean by saying " two vecotrs u<1,2,3> and v=<2,3,2> determine a plane in space Does that mean they are on the planes or just two position vectors that determine the two points on the plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh. It's saying that any two vectors that are linearly independent (not parallel) will define a plane.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or rather, that those two vectors are not parallel and therefore define a plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can also picture the tips of those vectors as lying in the plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so they are not parallel but "in the plane"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right. They are parallel to the plane, but not parallel to each other.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok,, i have thought of using cross product

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good idea. What will that tell you?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the normal vector of the plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0indeed. What does it mean to be normal to a plane?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any vectors parallel to the plane, but not necessarily in the plane, will have a 0 dot product with the the normal vector?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any vector parallel to the plane will be in the plane

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and yes, all the vectors in the plane are orthogonal to the normal vector of the plane (the dot product of the vector and the normal will be 0)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why any vector parallel to the plane will be in the plane?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry this is a new idea to me...i am kinda dumb right now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, since the plane is given by two vectors

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it intersects the origin

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0because vectors start at the origin, and end on the point specified with <x,y,z>

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, vectors are simply directions, not positions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So all the vectors in the plane will be orthogonal to the normal of the plane.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok got it :) thanks~~~~!!!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i have one more question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the textbook i am using talks about displacement vector, which is defined by the difference of two points in space, and it does not go through the origin... so are there different kinds of vectors?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No, vectors can be moved around

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0they have a magnitude and a direction, but not a position

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But there are not really different kinds of vectors (except when you're talking about vectors in different vector spaces)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh so you can always visualize a vector starting at the origin and points toward some direction,,,kk i think i get it now Thanks :)
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