Proof of dot product formula. - Mathematics Stack Exchange
2020年8月9日 · The dot product essentially "multiplies" 2 vectors. If the 2 vectors are perfectly aligned, then it makes sense that multiplying them would mean just multiplying their magnitudes. It's when the angle between the vectors is not 0, that things get tricky.
Dot product cancellation - Mathematics Stack Exchange
2019年10月28日 · $\begingroup$ @ThomasShelby The dot product of two vectors is equal to zero only if one is equal to zero ...
What does the dot product of two vectors represent?
2014年5月23日 · The dot product tells you what amount of one vector goes in the direction of another. For instance, if you pulled a box 10 meters at an inclined angle, there is a horizontal component and a vertical component to your force vector.
linear algebra - difference between dot product and inner product ...
The real dot product is just a special case of an inner product. In fact it's even positive definite, but general inner products need not be so. The modified dot product for complex spaces also has this positive definite property, and has the Hermitian-symmetric I mentioned above. Inner products are generalized by linear forms. I think I've ...
geometry - Proving that the dot product is distributive?
2015年1月18日 · I know that one can prove that the dot product, as defined "algebraically", is distributive. However, to show the algebraic formula for the dot product, one needs to use the distributive property in the geometric definition.
Proof for Derivative of Dot Product - Mathematics Stack Exchange
In Taylor's Classical Mechanics, one of the problems is as follows: (1.9) If $\\vec{r}$ and $\\vec{s}$ are vectors that depend on time, prove that the product rule for differentiating products app...
Euclidean distance and dot product - Mathematics Stack Exchange
I've been reading that the Euclidean distance between two points, and the dot product of the two points, are related. Specifically, the Euclidean distance is equal to the square root of the dot product. But this doesn't work for me in practice. For example, let's …
Square of Vector Dot Product - Mathematics Stack Exchange
2018年10月9日 · Representation of dot product of a vector. 0. Dot product of vectors. 4. Dot product of a vector and del ...
What can we say if the dot product of two vectors is equal to 1
2017年3月20日 · If you already know the vectors are pointing in the same direction, then the dot product equaling one means that the vector lengths are reciprocals of each other (vector b has its length as 1 divided by a's length). For example, 2D vectors of (2, 0) and (0.5, 0) have a dot product of 2 * 0.5 + 0 * 0 which is 1.
geometry - How to convert a dot product of two vectors to the …
2017年4月15日 · I've learned that in order to know "the angle" between two vectors, I need to use Dot Product. This gives me a value between $1$ and $-1$. $1$ means they're parallel to each other, facing same direction (aka the angle between them is $0^\circ$). $-1$ means they're parallel and facing opposite directions ($180^\circ$).