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In math, a "vector field" is an abstract term for a set, and a number of operations, that have specific properties. Matrices of the same size, for example, all 3 x 2 matrices, combined with matrix addition and multiplication by a scalar, happens to have all those properties. You may want to read an introductory Linear Algebra book for more details.
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What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
What are the applications of vector algebra and vector calclus?
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
What is the difference between unit vectors and column vectors?
a unit vector is any vector with length or absolute value 1. A column vector is any vector written in a column of since we say an mxn matrix is m rows and n columns, a column vector is mx1 matrix.
Can a vector be less than its magnitude?
For a start, you can't compare a vector with a scalar, so you can't really compare a vector with its magnitude, either. To say which is larger, you can't even compare one vector with another - you can only compare their magnitudes.
Which of these references a velocity (not speed)?
I would say vector
Is mosquito a vector?
I would say yes, as it can carries Malaria.
What can you say about two vectors if vector A vector B 0?
Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
How do vector components compare in size to the vector from which they came?
That all depends on the angles between the vector and the components. The only things you can say for sure are: -- none of the components can be greater than the size of the vector -- the sum of the squares of the components is equal to the square of the size of the vector
What does it mean when we say a vector is scaled?
It means that the direction of the vector is that same as before but the magnitude has been changed - by a scalar factor.
What are the applications of vector algebra and vector calclus?
Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
What is the difference between unit vectors and column vectors?
a unit vector is any vector with length or absolute value 1. A column vector is any vector written in a column of since we say an mxn matrix is m rows and n columns, a column vector is mx1 matrix.
Can a vector be less than its magnitude?
For a start, you can't compare a vector with a scalar, so you can't really compare a vector with its magnitude, either. To say which is larger, you can't even compare one vector with another - you can only compare their magnitudes.
Why do we say that velocity is a vector and speed is not a vector?
Velocity is a vector because it has both magnitude (speed) and direction. Speed, on the other hand, is a scalar quantity that only has magnitude. Vector quantities require both magnitude and direction to be fully described.
Is distance a vector quanity?
Distance is a scalar quantity, not a vector quantity. Scalars have only magnitude, while vectors have both magnitude and direction. Distance measures the length between two points and does not specify the direction of the displacement.
What does a vector involve?
A vector is a two part quantity. A vector includes both a magnitude (often a distance or a force) and a direction that the magnitude is in. Most of the population deals with scalar quantites, such as 10 miles or 5 pounds. But if you were to say 10 miles northwest, you would be giving a vector.
How do you find a normal vector?
A normal vector is a vector that is perpendicular or orthogonal to another vector. That means the angle between them is 90 degrees which also means their dot product if zero. I will denote (a,b) to mean the vector from (0,0) to (a,b) So let' look at the case of a vector in R2 first. To make it general, call the vector, V=(a,b) and to find a vector perpendicular to v, i.e a normal vector, which we call (c,d) we need ac+bd=0 So say (a,b)=(1,0), then (c,d) could equal (0,1) since their dot product is 0 Now say (a,b)=(1,1) we need c=-d so there are an infinite number of vectors that work, say (2,-2) In fact when we had (1,0) we could have pick the vector (0,100) and it is also normal So there is always an infinite number of vectors normal to any other vector. We use the term normal because the vector is perpendicular to a surface. so now we could find a vector in Rn normal to any other. There is another way to do this using the cross product. Given two vectors in a plane, their cross product is a vector normal to that plane. Which one to use? Depends on the context and sometimes both can be used!
