Question

Find a vector a with representation given by the directed line segment AB. Draw AB and the equivlent representation starting the origin. A(4,0,-2), B(4,2,1)

Answer 1

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.

$\vec a$ 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 $A(x_1,y_1,z_1)\ and\ B(x_2,y_2,z_2)$ is represented as:

$\overrightarrow {AB}=(x_2-x_1)\vec i+(y_2-y_1)\vec j+(z_2-z_1)\vec k$

Now, using the given points, the vector 'a' with endpoints A and B can be written as:

$\vec a=(x_2-x_1)\vec i+(y_2-y_1)\vec j+(z_2-z_1)\vec k$

$\vec a=(4-4)\vec i+(2-0)\vec j+(1-(-2))\vec k$

$\vec a=0\vec i+2\vec j+3\vec k$

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.