Question

I'm really stuck with this and would love some help:
u and v are vectors such that:
(u - v)(3u + 5v) = -114
(u-v)(u + 2v) = -45
uv=4
(These three are dot products)
Therefore |u X v| = ? (vector multiplication)
Thank you!

Answer 1

hint: to solve ur question
Let’s consider a vector v whose initial point is the origin in an xy - coordinate system and whose terminal point is . We say that the vector is in standard position and refer to it as a position vector. Note that the ordered pair defines the vector uniquely. Thus we can use to denote the vector. To emphasize that we are thinking of a vector and to avoid the confusion of notation with ordered - pair and interval notation, we generally write
v = < a, b >.
The coordinate a is the scalar horizontal component of the vector, and the coordinate b is the scalar vertical component of the vector. By scalar, we mean a numerical quantity rather than a vector quantity. Thus, is considered to be the component form of v. Note that a and b are NOT vectors and should not be confused with the vector component definition.

Now consider with A = (x1, y1) and C = (x2, y2). Let’s see how to find the position vector equivalent to . As you can see in the figure below, the initial point A is relocated to the origin (0, 0). The coordinates of P are found by subtracting the coordinates of A from the coordinates of C. Thus, P = (x2 - x1, y2 - y1) and the position vector is .
It can be shown that and have the same magnitude and direction and are therefore equivalent. Thus, = = < x2 - x1, y2 - y1 >.

The component form of with A = (x1, y1) and C = (x2, y2) is
= < x2 - x1, y2 - y1 >.

Answer 2

Thanks but that doesn't really address the question

Answer 3

see it carefully