AMDM Question (Mathematics)

Question

A vector starts at point (5, -4) and ends at point (0, -8). What is the vertical component of the vector?

Answer 1

Solution:

A vector starts at point A (5, -4) or ( x_1, y₁) and ends at point B (0, -8) or at ( x_2, y_{2) .}  What is the vertical component of the vector?

The vertical component of the vector V_y is simply y₂ - y₁ = -8 -(-4) = -8 +4 = -4 note the negative sign indicate that the vector moving from point A to B is 4 units down , if the vector was moving from B to A then V_y = y₁-y₂

= -4 -(-8) = -4+8 = +4 and the positive sign indicates that the vector is moving 4 units up. This makes sense because point B is below point A on a cartesian system of axes. Please remember that a vector in space has both a magnitude and a direction that must be indicated by an arrow with vector tail at the start point and and vector head where the arrow is at the end point.