Question

Find a vector with the initial point A and terminal point B. Then, determine the unit vector in the direction of AB. Choose from the following options:

a) Vector AB: ⟨X,Y,Z⟩, Unit Vector: ⟨P,Q,R⟩
b) Vector AB: ⟨U,V,W⟩, Unit Vector: ⟨S,T,U⟩
c) Vector AB: ⟨M,N,O⟩, Unit Vector: ⟨K,L,M⟩
d) Vector AB: ⟨D,E,F⟩, Unit Vector: ⟨C,B,A⟩
e) Vector AB: ⟨H,I,J⟩, Unit Vector: ⟨G,H,I⟩

Answer 1

To find the vector AB, subtract the coordinates of point A from the coordinates of point B. To find the unit vector in the direction of AB, divide the vector AB by its magnitude.

Step-by-step explanation:

To find the vector AB, we subtract the coordinates of point A from the coordinates of point B. Let's say the coordinates of A are (x1, y1, z1) and the coordinates of B are (x2, y2, z2). Then, the vector AB is given by AB = ⟨x2 - x1, y2 - y1, z2 - z1⟩.

To determine the unit vector in the direction of AB, we divide the vector AB by its magnitude. Let's say the magnitude of AB is M. Then, the unit vector in the direction of AB is given by ⟨(x2 - x1)/M, (y2 - y1)/M, (z2 - z1)/M⟩.