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The triangle law of vector addition is a fundamental law that is fundamental to the construction of vectors. It’s an interesting law, but it can be really confusing. A lot of questions arise when we hear it because it can be applied to any vector (vector is a type of 3D object). I’m going to try to explain the triangle law as a primer, and then I will explain some common misconceptions.
The triangle law of vector addition states that the sum of any three vectors is equal to zero. It can be applied to any type of 3D object such as a cube, or to any type of vector (in 3D space). In most cases, when we add vectors, that is the only thing we are doing.
If we have three vectors, and we want to add their sum, we just add them together. If we want to subtract, we subtract the vector from the vector. If we add two vectors, we will always have to use the dot product or the cross product. If we have two non-zero vectors, the dot product or cross product will not be zero. If two vectors are zero, then the dot product or cross product will be zero as well.
If any two vectors are equal, the dot product will be zero, but the cross product will be non-zero. So if two vectors are zero, the dot product and the cross product will both be zero. So for example, when I say “I have three vectors,” that means that I have three vectors that are equal. So then the dot product and the cross product will both be zero.
So if your vector sum is zero, then the dot product and the cross product will all be zero. If your vector product is zero, then the dot product and the cross product will be zero, and if both the dot product and the cross product are zero, then the vectors are equal. So for example, if I have three vectors, then I have three vectors that are equal. So then the dot product and the cross product will both be zero.
Which is not to say that this is always the case. If the vectors are in a line, then the dot product and the cross product will be zero. It’s just that this situation is rare. If the vectors are parallel or perpendicular to each other, then the dot product and the cross product will both be zero. It’s called a linear combination of zero vectors.
In this class, we are going to solve some problems with vectors and then move on to discuss how to solve those same problems with matrices. But first, a bit of background about vectors and matrices. Both vectors and matrices are really small. The size of the vector is the number of elements in the vector. The size of the matrix is the number of rows and columns.
A vector is like a little blob of information. We know what it is because we know what it isn’t. A vector is just a bunch of numbers. So when we talk about a “vector” we are really talking about a bunch of numbers in a row or column.
This little blob of information is called a “vector.” We can think of vectors as being the basis of a matrix. A matrix is a bunch of numbers arranged in rows and columns. The order of the numbers in a matrix depends on how the matrix is built.
So when we talk about matrices we are actually talking about the order of the numbers in a vector. So matrices are just a bunch of numbers arranged in rows and columns.