Question

A shopper pushing a cart through a market follows directions to the earned goods and moves through a displacement 8.00i m down one aside. He then makes a 90.0^oturn and moves 3.00 m along the y axis. He then makes another 90.0^o turn and moves 4.00 m along the x axis . Every shopper who follows these direction correctly ends up 5.00 m from the starting point.

Short answer

Impossible because 12.4 > 5.00

Step-by-step solution

Definition of vector

A vector is a quantity that has both a direction and a magnitude, and is used to determine the relative location of two points in space.

Step 2:Formula

f vector A = a₁i + a₂j + a₃k and vector B = b₁i + b₂j + b₃k then the displacement of AB = (b₁ - a₁)i + (b₂ - a₂)j + (b₃ - a₃)k

If vector A = x₁i + y₁j + z₁k and vector B = x₂i + y₂j + z₂k then the displacement of

The Pythagorean theorem and the definition of tangent will use for calculation

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

Calculation

Each shopper must make a choice whether to turn 90^o to the left or right, each time he or she makes a turn. One set of such choices, following the rules of the problem, results in the shopper heading in the positive y direction and then again in the positive x direction.

So, the sum of magnitude is

$$\begin{gathered} d=8.00i+3.00j+4.00i=12.00i+3.00j \\ d=\sqrt{{\left(12.00\right)}^2+{\left(3.00\right)}^2} \\ d=12.4m \\ 12.4>5.00 \end{gathered}$$