A <-9, 7>
B< -7,12>
Find AB in component from and the magnitude?
(2,5) component so so sqrt29 magnitude of the vector?Is this correct?
Your symbols make no sense to me.
Do you mean A is at (-9 , 7 ) and B is at (-7 , 12 ) ????
in that case the length of the x component of vector AB is
-7 - -9 = +2
and the y component is
12 - 7 = 5
so AB = 2 i + 5 j as you said and |AB| = sqrt (4+25) as you said
yes, thank you, those are for the vectors.
To find the component form of vector AB, you subtract the coordinates of point A from the coordinates of point B.
For AB, we have B - A:
(-7, 12) - (-9, 7) = (-7 + 9, 12 - 7) = (2, 5)
So, the component form of vector AB is (2, 5).
To find the magnitude of vector AB, you can use the distance formula or the Pythagorean theorem.
Using the distance formula, the magnitude of vector AB is given by:
|AB| = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
= sqrt[(2 - 0)^2 + (5 - 0)^2]
= sqrt[4 + 25]
= sqrt[29]
Therefore, the magnitude of vector AB is sqrt(29).
Yes, your answer of (2, 5) for the component form and sqrt(29) for the magnitude is correct.