Let the vector \mathbf{v}v have an initial point at (1, -2)(1,−2) and a terminal point at (0, 0)(0,0). Plot the vector \mathbf{v}v and afterwards follow the guided steps to analyze the vector.

Given that the initial point of the vector is (1,-2) and the termination point of the vector is (0,0).

So, the tail of the vector is at point (1,-2) and the head of the vector is at (0,0). The vector, , has been shown in the figure.

The magnitude of the vector:

The direction of a vector is the angle made by a vector with the positive direction of the x-axis.

From the figure,

Hence, the required vector having a magnitude and direction has been shown in the figure.

(8r^6s^3 – 9r^5s^4 + 3r^4s^5) – (2r^4s^5 – 5r^3s^6 – 4r^5s^4)

= 8r^6s^3 – 9r^5s^4 + 3r^4s^5 – 2r^4s^5 +  5r^3s^6 + 4r^5s^4

= 8r^6s^3 – 9r^5s^4 +  4r^5s^4 + 3r^4s^5 – 2r^4s^5 +  5r^3s^6

= 8r^6s^3 – 5r^5s^4 + r^4s^5  +  5r^3s^6

Step-by-step explanation:

Its simple math.