向量运算(vector operations)
基本代数定律延伸至向量。包括加法、减法以及三种乘法。两个向量的加总是第三个向量，利用原来两个向量做边长的平行四边形的对角线。当向量乘以正数，大小乘以该数的量，方向维持不变（如果是负数，则反向）。向量a乘以另一个向量b的结果有内积和外积，内积写成a . b，外积写成a × b。内积是实数，又称数量积，等於两个向量的长度a（|a|）、b（|b|）及两者夹角（Θ）余弦的乘积，表示为：a . b = |a| |b| cosΘ。如果两个向量垂直的话，内积为零。外积是第三个向量（c），又称向量积，垂直於原来向量构成的平面。向量c的大小等於向量a和b的长度与两者之间夹角（Θ）正弦的乘积：c = |a| |b| sin Θ。组合律与交换律在向量加法与内积上有效。外积适用组合律，不适用交换律。
English version：
vector operations
Extension of the laws of elementary algebra to vectors. They include addition, subtraction, and three types of multiplication. The sum of two vectors is a third vector, represented as the diagonal of the parallelogram constructed using the two original vectors as sides. When a vector is multiplied by a positive scalar (I.e., number), its magnitude is multiplied by the scalar and its direction remains unchanged (if the scalar is negative, the direction is reversed). The multiplication of a vector a by another vector b leads to the dot product, written a · b, and the cross product, written a × b. The dot product, also called the scalar product, is a scalar real number equal to the product of the lengths of vectors a (|a|) and b (|b|) and the cosine of the angle (θ) between them: a · b = |a| |b| cos θ. This equals zero if the two vectors are perpendicular (see orthogonality). The cross product, also called the vector product, is a third vector (c), perpendicular to the plane of the original vectors. The magnitude of c is equal to the product of the lengths of vectors a and b and the sine of the angle (θ) between them: c = |a| |b| sin θ. The associative law and commutative law hold for vector addition and the dot product. The cross product is associative but not commutative.