Suppose v⇀ is a vector with initial point (3,− 4) and terminal point (− 4,2). write v⇀ as a linear combination of the standard unit vectors i⇀= ⟨1,0⟩ and j⇀= ⟨0,1

Standard vector is of the form ai+bj

v⇀  = (-4-3)i + (2- -4)j

v⇀ = - 7i + 6j

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)