Mathematics 10 — Exercise Review · Q2 (i)

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.

   $$-12\times î+0\times ĵ-(7\times î+7\times ĵ)$$

2. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 7=-7$$

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

   $$-12-7=-19$$

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

   $$0-7=-7$$

5. Write the two calculated components as a vector.

   $$-19\times î-7\times ĵ$$

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

   $$\left[\begin{array}{c}-19\\ -7\end{array}\right]$$

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

   $$\sqrt{{\left(-19\right)}^2+{\left(-7\right)}^2}$$

8. Square the horizontal component, including its sign.

   $${\left(-19\right)}^2=361$$

9. Square the vertical component, including its sign.

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

10. Add these two squares.

    $$361+49=410$$

11. Take and simplify the positive square root.

    $$\sqrt{410}=\sqrt{410}$$

Answer

The final answer is shown below.