Answer:
The component form of the vector is v = -7·i + 2·j
Step-by-step explanation:
The given parameters are;
The coordinates of the initial point = P(4, 5)
The coordinates of the point after the translation by the vector, v = P'(-3, 7)
Therefore, we have;
The horizontal component of the vector, vₓ = (-3) - 4 = -7
The vertical component of the vector, [tex]v_y[/tex] = 7 - 5 = 2
The magnitude of the translation, v = √([tex]v_y[/tex]² + vₓ²) = √((-7)² + 2²) = √53 ≈ 7.28
Therefore, the component form of the vector, v, is given as follows;
v = vₓ·i + [tex]v_y[/tex]·j
Substituting the known values of vₓ and [tex]v_y[/tex] gives;
v = -7·i + 2·j
The component form of the vector is v = -7·i + 2·j.
