Answer:
The vector AB with endpoints A(4, 0, -2) and B(4, 2, 1) is drawn below.
The equivalent representation of the vector AB from origin is also drawn below.
[tex]\vec a[/tex] is <0, 2, 3>
Step-by-step explanation:
Given:
Point A is given as: A(4, 0, -2)
Point B is given as: B(4, 2, 1)
Now, a vector AB with endpoints [tex]A(x_1,y_1,z_1)\ and\ B(x_2,y_2,z_2)[/tex] is represented as:
[tex]\overrightarrow {AB}=(x_2-x_1)\vec i+(y_2-y_1)\vec j+(z_2-z_1)\vec k[/tex]
Now, using the given points, the vector 'a' with endpoints A and B can be written as:
[tex]\vec a=(x_2-x_1)\vec i+(y_2-y_1)\vec j+(z_2-z_1)\vec k[/tex]
[tex]\vec a=(4-4)\vec i+(2-0)\vec j+(1-(-2))\vec k[/tex]
[tex]\vec a=0\vec i+2\vec j+3\vec k[/tex]
Therefore, the vector 'a' is <0, 2, 3>
The vector AB with endpoints A(4, 0, -2) and B(4, 2, 1) is drawn below.
The equivalent representation of the vector AB from origin is also drawn below.
In this exercise we have to have a knowledge of vectors, in order to be able to represent them, so we have to:
[tex]A(4, 0, -2)\\B(4, 2, 1)\\AB(0, 2, 3)[/tex]
So knowing that it was informed that the values of each vector are represented by:
Now, a vector AB with endpoints is represented as:
[tex]A(x_1, y_1, z_1)\\B(x_2, y_2, z_2)\\AB=(x_2-x_1)+(y_2-y_1)+(z_2-z_1)[/tex]
Now, using the given points, the vector 'AB' with endpoints A and B can be written as:
[tex]AB= (x_2-x_1)+(y_2-y_1)+(z_2-z_1)\\AB=(4-4)+(2-0)+(1+2)\\AB(0, 2, 3)[/tex]
See more about vectors at brainly.com/question/13188123
