Answer: To write the vector V in terms of the unit vectors i and j, we need to find the components of the vector V.
The components of a vector from P1 to P2 can be obtained by subtracting the coordinates of P1 from the coordinates of P2.
Given:
P1 = (-8, 7)
P2 = (-2, -8)
The components of vector V (Vx, Vy) are given by:
Vx = P2x - P1x
Vy = P2y - P1y
where P2x and P2y are the x and y coordinates of P2, respectively, and P1x and P1y are the x and y coordinates of P1, respectively.
Let's calculate the components of vector V:
Vx = -2 - (-8) = -2 + 8 = 6
Vy = -8 - 7 = -15
So, the components of vector V are Vx = 6 and Vy = -15.
Now, we can write vector V in terms of the unit vectors i and j:
V = Vx * i + Vy * j
Substitute the values of Vx and Vy:
V = 6 * i + (-15) * j
Therefore, the vector V from initial point P1 to terminal point P2 is written in terms of i and j as:
V = 6i - 15j