Calculus and vectors

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Vector AB is a vector whose tail is at (-4,2) and whose head is at (-1,3).
Calculate the magnitude of vector AB
Determine the coordinates of point D on vector CD, if C (-6,0) and vector CD= vector AB.

Please I need some help. Is there a formula to solve this? Pls help

• Calculus and vectors -

I will let A be (-4,2) and B(-1,3)
vector AB = ( -1+4 , 3-2)
= (3,1)
magnitude of AB = √(3^2 + 1^2) = √10

let D be (x,y)
the vector CD = (x+6, x-0) = (x+6 , y)
but if vector AB = vector CD
then x+6 = 3
x = -3
and y = 1
so point D is (-3,1)

in general if A is the point (a,b) and B is the point (c,d)
then vector AB = ( c-a , d-b)
and vector BA = ( a - c, b - d)

note that vector AB = - vector BA

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