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• Once you have such a formula, you do the dot product with this vector field, which is not the same as that one.

一旦得到一个这样计算式向量前面这个一样

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• This expression not only contains the term of dot product of velocity vector and temperature gradient, but also contains the dot product of velocity vector and the pressure gradient.

不仅速度矢量温度梯度矢量含有速度矢量压力梯度矢量项。

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• The dot product and matrices. Read Chapter3 through3.7 and do exercises.

矩阵阅读第三章3.7以及练习题

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• And I can rewrite this in vector form as the gradient dot product the amount by which the position vector has changed.

可以这些向量形式重新写下来,就是梯度向量位置改变

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• The dot product, being the product of three scalars, is a scalar.

三个标量乘积，所以是个标量

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• But, you will see that notation somehow helps to make it more straightforward So, what is dot product?

但是发现,这个方法问题简单,那么什么”？

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• What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.

我们沿着曲线一点上，取向量向量

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• But now the power that I have to generate is the dot product between the force and the velocity.

现在产生,功率速度,标量

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• It's the dot product between the normal vector of a plane and the vector along the line.

平面向量,沿直线向量

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• There are two ways that we multiply vectors and one is called the "dot product" often also called the scalar product.

矢量乘法,一种叫做“,通常被叫作数量

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• I'm going to teach you-- - just like with the dot product-- two methods.

一样-,我会教你们-,两种方法

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• There is another way that you can find the dot product.

另一个定义,方法

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• Dot Product of two vectors.

两个向量乘积

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• This function tests whether dot product of two quaternions is close to 1.0.

这个函数测试两个四元是否接近1.0

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• The dot product between two rotations.

两个旋转之间

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• This function tests whether dot product of two quaternions is less than 1.0.

这个函数测试两个四元是否接近1.0

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• These two vectors are perpendicular exactly when their dot product is zero.

乘的数量零时,两个向量垂直

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• And since work is a dot product between force and the direction that it travels, neither the tension nor the normal force does any work.

既然运动,路程,不管是张力还是,法向都不做功

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• Since scalars are independent of the coordinate system, the dot product of two vectors is called a scalar invariant.

因为标量坐标系无关，故两个矢量称为标量不变量

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• So, product rule is OK for taking the derivative of a dot product.

那么乘积法则求导没问题

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• Now you have two vectors, but the vector dot product requires normalized vectors to return usable results.

现在两个向量向量用到标准化向量

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• And, if you want to find what goes in a given slot here, then you just look to its left and you look above it, and you do the dot product between these guys.

如果找到,这个位置是什么,往上看然后它们

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• Well, we've learned how to detect whether two vectors are perpendicular to each other using dot product.

我们怎么,来判断两个向量是否垂直

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• If I take the dot product But now, what does it mean that the dot product between OP and A is zero?

如果OP·A得到了,那么OPA点积0代表什么呢？

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• So, that's going to be one of the main uses of dot product.

就是一个主要用途

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• The dot product of a pseudo vector and a vector is called a pseudoscalar.

一个矢量一个矢量标识称为赝标量

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• And that is if I keep this force constant for that short amount of time is the dot product times the velocity, because dr/dt is simply the velocity of that object.

如果短时内,保持,乘以速率因为dr/dt就是,物体速率

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• After the formula of documents are used to rewrite elements of Jacobian matrix, the vector cross product is changed into the vector dot product in Jacobian matrix.

利用现有公式可比矩阵中的元素进行改写矢量变为矢量乘。

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• And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.

例如某些情况下，如果已知向量曲线相切,或者一个常数等等,那么结果将简单

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• And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.

例如某些情况下，如果已知向量曲线相切,或者一个常数等等,那么结果将简单

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