No. The dot product is also called the scalar product and therein lies the clue.
It can be any direction. It depends on the magnitudes and directions of the two original vectors.
vectors
Any measurement in which the direction is relevant requires vectors.
No. Only in the equilateral case. And then they will only be equal in magnitude, not direction.
Unit vectors are perpendicular. Their dot product is zero. That means that no unit vector has any component that is parallel to another unit vector.
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
No. A vector is any measurement that includes a direction, for example velocity, momentum, acceleration, or force.
The vector is body fluid exchangeCorrection:Bodily fluids are not technically vectors. A vector is a living organism, usually a mosquito or tick, that is capable of transmissing disease. To date, no vectors have been identified as causing HIV infection.
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
An object with a constant acceleration and velocity in the same direction will have both vectors pointing in the same direction. This occurs when an object is moving in a straight line with a constant speed while its velocity is also increasing at a constant rate.
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
I'll assume you are referring to the inverse of the most common process of vector multiplication, namely the formation of an inner product, also called a scalar product or dot product, between two vectors of the same size. In this operation, vectors with, for example, components (a,b,c,d) and (e,f,g,h) must be pairwise multiplied and summed, to arrive at the scalar result ae + bf + cg + dh. Any two ordinary vectors of matching size (number of components) can be "multiplied" to get an inner product. (There is another kind of multiplication of two 3-vectors called the cross-product, which is sometimes invertible, but because the cross-product only works with two vectors in 3-space, it does not seem useful to discuss the cross-product further in the context of general vector division. Similarly, one could individually multiply the components of the two vectors to get a sort of third vector. Although that operation would be invertible under some conditions, I am not aware of any meaning, or physical significance, for the use of that technique. Since the result of taking the inner product of two vectors is a scalar, that is, a single real number, most of the information about the two vectors is lost during the computation. The only information retained by the inner product is the magnitude of the projection of one vector A onto the direction of another vector B, multiplied by the magnitude of B. But division is the inverse operation of multiplication. In a sense, division undoes the work of a previous multiplication. Since all information about the direction of each vector is discarded during the calculation of an inner product, there is not enough information remaining to uniquely invert this operation and bring back, say, vector A, knowing vector B and the value of the scalar product.