Question

Find a vector a with representation given by the directed line segment AB. A(2, 0, −2), B(2, 5, 1)

Answer 1

The directed line segment AB of vector representation is AB = ( 0, 5,3).

According to the statement

we have given that the vector and the two points A and B and we have to find the vector representation of  AB.

So, For this purpose, we have given that the points.

A(2, 0, −2), B(2, 5, 1)

Here $A(2, 0, -2) = A(x_{1} , y_{1} , z_{1} )$

And

$B(2, 5, 1) = B(x_{2} ,y_{2} ,z_{2} )$

And we have to find the Line segment AB.

So, The value of AB is

$AB = (x_{2} - x_{1} , y_{2} - y_{1} , z_{2} - z_{1} )$

So to find this substitute the values in it then

Then the values becomes of AB is

AB = ( 2-2, 5-0, 1+2 )

AB = ( 0, 5,3).

The value of the AB is AB = ( 0, 5,3).

So, The directed line segment AB of vector representation is AB = ( 0, 5,3).

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