Find Vector u Midpoint (-2,-4,0) to (10,6,0) and (1,-4,4) to (5,8,-10)

[~Sam~]

Homework Statement

Find the vector u=(xyz) whose

(i) initial point is the midpoint of (-2,-4,0) and (10,6,0)

(ii) terminal point is the midpoint of (1,-4,4) and (5,8,-10)

Homework Equations

I know the midpoint for two vectors from say..P to Q is P+ (1/2) (Q1-P1 Q2-P2, Q3-P3)

The Attempt at a Solution

I can find mids for both..but am confused by the initial midpoint to terminal midpoint..what else do I need?

 

[lanedance]

i think read start & end of the vector u, for initial & terminal respectively. The midpoint just let's you find where they are

 

[Architeuthis Dux]

To find the vector u, we first need to find the coordinates of the initial and terminal points. The initial point will be the midpoint of (-2,-4,0) and (10,6,0), which can be found using the formula (P+Q)/2, where P and Q are the coordinates of the two points. Plugging in the coordinates, we get (-2+10)/2 = 4 for the x-coordinate, (-4+6)/2 = 1 for the y-coordinate, and (0+0)/2 = 0 for the z-coordinate. Therefore, the initial point is (4,1,0).

Similarly, the terminal point will be the midpoint of (1,-4,4) and (5,8,-10), which can be found using the same formula. Plugging in the coordinates, we get (1+5)/2 = 3 for the x-coordinate, (-4+8)/2 = 2 for the y-coordinate, and (4-10)/2 = -3 for the z-coordinate. Therefore, the terminal point is (3,2,-3).

Now, we can use the coordinates of the initial and terminal points to find the vector u. The vector u will be the difference between the terminal point and the initial point, which can be found by subtracting the coordinates of the initial point from the coordinates of the terminal point. Therefore, the vector u is (3-4, 2-1, -3-0) = (-1,1,-3).

In summary, the vector u whose initial point is the midpoint of (-2,-4,0) and (10,6,0) and terminal point is the midpoint of (1,-4,4) and (5,8,-10) is (-1,1,-3).