The position vector of m in the same plane are as the point a and b is given by m=1÷2(a+b).if the vector A(-4,-3),B(2,-1).What is the direction and the relationship of vector AM and vector BM
To find the direction and relationship between vector AM and vector BM, let's start by finding the position vectors of points A, B, and M.
Given: A(-4, -3) and B(2, -1)
The position vector m in the same plane as points A and B is given by:
m = (1/2)(a + b)
Substituting the values:
m = (1/2)(-4, -3) + (2, -1)
Simplifying:
m = (-2, -1.5) + (2, -1)
= (0, -2.5)
Therefore, the position vector of point M is (0, -2.5).
Now that we have the position vectors of points A, B, and M, we can find the vectors AM and BM.
Vector AM can be obtained by subtracting vector A from vector M:
AM = M - A
= (0, -2.5) - (-4, -3)
= (0 + 4, -2.5 + 3)
= (4, 0.5)
Similarly, vector BM can be obtained by subtracting vector B from vector M:
BM = M - B
= (0, -2.5) - (2, -1)
= (0 - 2, -2.5 + 1)
= (-2, -1.5)
To find the direction and relationship between AM and BM, we can compare their components.
Comparing the x-components, we have:
AMx = 4
BMx = -2
Since AMx > BMx, the x-component of vector AM is greater than the x-component of vector BM.
Comparing the y-components, we have:
AMy = 0.5
BMy = -1.5
Since AMy < BMy, the y-component of vector AM is smaller than the y-component of vector BM.
Therefore, we can conclude that vector AM is in the positive x-direction and vector BM is in the negative x-direction. Additionally, vector AM is in the positive y-direction and vector BM is in the negative y-direction.