Mathematics 10 — Exercise Review · Q2 (ii)

Full question

Find the magnitude of vector AB.

Step-by-step solution

1. Vector from the first point to the second is endpoint minus starting point.

   $$2\times î+11\times ĵ-(9\times î+3\times ĵ)$$

2. Subtract the matching starting coordinate from the endpoint coordinate.

   $$2-9=-7$$

3. Subtract the matching starting coordinate from the endpoint coordinate.

   $$11-3=8$$

4. Write the two calculated components as a vector.

   $$-7\times î+8\times ĵ$$

5. Use the horizontal and vertical components as the two perpendicular sides.

   $$\left[\begin{array}{c}-7\\ 8\end{array}\right]$$

6. Magnitude is the nonnegative square root of the sum of component squares.

   $$\sqrt{{\left(-7\right)}^2+8^2}$$

7. Square the horizontal component, including its sign.

   $${\left(-7\right)}^2=49$$

8. Square the vertical component, including its sign.

   $$8^2=64$$

9. Add these two squares.

   $$49+64=113$$

10. Take and simplify the positive square root.

    $$\sqrt{113}=\sqrt{113}$$

Answer

The final answer is shown below.