Question

given the initial ( 0 , − 2 ) and terminal ( 3, 6 ) points of a vector, how do you write a linear combination of the standard unit vector ˆ i and ˆ j ? socratic.org

Answer 1

Answer:

Explanation:

Given that,

The initial point A=(0,-2)

And the final point B=(3,6)

O is a reference point (0,0)

OA=r1=(0,-2)

OB=r2=(3,6)

Then we want to find their combination vector i.e AB.

AB is given as position vector B - position vector A

So, AB=OB-OA

AB=r2-r1

AB=(3,6)-(0,-2). Note -×-=+

Then, AB=(3-0,6--2)

AB=(3,6+2)

AB=(3,8)

In vector form

AB=3•i +8•j