The dot product has the cancellation property. This statement is actually False.
In vector algebra, while the dot product of two vectors yields a scalar quantity and provides some information about the vectors, it does not necessarily equate to the two vectors being equal, even if their dot products with the same vector are the same.
The equality of dot products (ū.y = ū.w) does not directly translate to the equality of the vectors themselves (y = w). The dot product is a measure of how much one vector goes in the direction of another, and equal dot products do not necessarily imply that the two vectors (y and w) themselves are equal.
Dot products are affected by both the magnitudes of the vectors and the angle between them. Two entirely different vectors can have the same dot product with a third vector if the product of their magnitude and the cosine of their respective angles with the third vector is the same. So, the same dot product does not necessarily mean the two vectors are identical.
Hence, the cancellation property does not hold true in the context of dot products of vectors, which means that if ū.y=ū.w then y=w is not necessarily true, which makes the statement False.