Given that OA = 2i + 3j and OB = 3i - 2j. Find the magnitude of AB
I guess O is the origin and you want the vector from point A to point B
well from A to B in the x direction is 3 - 2 = 1
and from A to B in the y direction is -2 -3 = -5
so
sqrt (1^1 + 5^2) = sqrt 26
To find the magnitude of AB, we need to find the vector AB first by subtracting vector OA from vector OB.
AB = OB - OA
= (3i - 2j) - (2i + 3j)
= 3i - 2j - 2i - 3j
= (3 - 2)i + (-2 - 3)j
= i - 5j
Now, to find the magnitude of AB, we can use the formula:
|AB| = sqrt((x^2) + (y^2))
where x and y are the components of the vector AB.
In this case:
x = 1
y = -5
Thus, the magnitude of AB can be calculated as follows:
|AB| = sqrt((1^2) + (-5^2))
= sqrt(1 + 25)
= sqrt(26)
Therefore, the magnitude of AB is sqrt(26).