Point A=(1,3,4) and point B=(-2,2,0). Determine AB.
a) (3,1,4)
b) (-3,-1,-4)
c) (-1,5,4)
d) (1,5,4)
I chose answer C.
2. A goes from (2,1) to (4,-1) Determine the components of A.
a) (6,0)
b) (-2,2)
c) (2,-2)
d) (0,6)
I will assume that AB is a vector, then
AB = [-2-1 , 2-3 , 0-4]
= [ -3 , -1 , -4]
which is choice b)
For your second, do it the same way to get c)
Well, my dear human, let's do some mathemagic!
1. The distance between two points A and B can be found using the distance formula. So, let's do some calculations.
The x-coordinate difference is (1 - (-2)) = 3.
The y-coordinate difference is (3 - 2) = 1.
The z-coordinate difference is (4 - 0) = 4.
Putting it all together, AB = (3, 1, 4).
Now, moving on to the next question!
2. To find the components of A, we simply subtract the corresponding coordinates of the two points.
The x-coordinate difference is (4 - 2) = 2.
The y-coordinate difference is (-1 - 1) = -2.
Therefore, A = (2, -2).
And there you have it! So the correct answer is c) (2, -2). Keep smiling, my friend!
For question 2: The components of A can be determined by subtracting the x-coordinates and y-coordinates of the two points.
Coordinates of point 1: (2,1)
Coordinates of point 2: (4,-1)
Subtracting the x-coordinates, we get: 4 - 2 = 2
Subtracting the y-coordinates, we get: -1 - 1 = -2
Therefore, the components of A are (2, -2).
So the correct answer is c) (2, -2).
To determine the distance between two points, such as point A and point B in the first question, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula in three dimensions is:
d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Let's calculate the distance between points A and B using the given coordinates:
x1 = 1, y1 = 3, z1 = 4
x2 = -2, y2 = 2, z2 = 0
Plugging in the values into the distance formula:
d = √((-2 - 1)^2 + (2 - 3)^2 + (0 - 4)^2)
= √(9 + 1 + 16)
= √26
So the distance between points A and B is √26.
Now let's move on to the second question. The components of A can be determined using the coordinates of the given start and end points (2,1) and (4,-1).
The components of A are the differences between the respective coordinates. So:
x-component = 4 - 2 = 2
y-component = -1 - 1 = -2
Therefore, the components of A are (2, -2).
Please note that in the second question, we are not calculating distance, but rather finding the components of A based on the given points.