- #1
gtfitzpatrick
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- 0
Homework Statement
r.k where r=xi+yj+zk
The Attempt at a Solution
is the answer to this just z or is it x+y
Ok, good. So, presumably, this definition is for two vectors a=(a1,a2,a3) and b=(b1,b2,b3). Can you write your two vectors in this form?gtfitzpatrick said:Dot product of 2 vectors a.b is a1b1+a2b2+a3c3?
Hold on.. this doesn't agree with what you stated above. Have another think...gtfitzpatrick said:i think k.k = 0
The product of two vectors is a mathematical operation that results in a scalar, vector, or tensor quantity. It is used to determine the relationship between two vectors in terms of magnitude and direction.
There are three types of products of two vectors: dot product, cross product, and tensor product. The dot product results in a scalar quantity, the cross product results in a vector quantity, and the tensor product results in a tensor quantity.
The dot product of two vectors is calculated by multiplying the magnitude of one vector by the magnitude of the projection of the other vector onto the first vector. This can also be represented as the sum of the products of each component of the two vectors.
The cross product of two vectors is used to determine the direction of the perpendicular vector to the plane formed by the two original vectors. It is also used in calculating torque and determining the area of a parallelogram.
Yes, the product of two vectors can be negative. This is dependent on the angle between the two vectors, and can result in a negative scalar or a negative direction for the resulting vector.