Find the displacement vector from the point(0,3-1) to the point (-2,6,4)give your answer in i,j,k notation,also give the magnitude to the displacement
The displacement vector is (final)-(initial) where final and initial is i,j,k format.
-3i+3j+5k
To find the displacement vector from point A to point B, we need to subtract the coordinates of point A from the coordinates of point B.
Given:
Point A: (0, 3, -1)
Point B: (-2, 6, 4)
To find the displacement vector, we subtract the corresponding coordinates:
x-component: -2 - 0 = -2
y-component: 6 - 3 = 3
z-component: 4 - (-1) = 5
Therefore, the displacement vector from point A to point B is (-2, 3, 5).
To find the magnitude of the displacement vector, we can use the Euclidean distance formula:
Magnitude = √(x^2 + y^2 + z^2)
Substituting the values:
Magnitude = √((-2)^2 + 3^2 + 5^2)
= √(4 + 9 + 25)
= √38
Hence, the magnitude of the displacement vector is √38.