Mathematics 10 — Exercise 6.3 · Q10

Full question

A car enters with velocity 30ĵ and exits with 30î. Find the change in velocity.

Step-by-step solution

1. The orders match. Combine only entries in the same row and column.

   $$(\left[\begin{array}{c}30\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 30\end{array}\right])$$

2. Entry (1,1): subtract the corresponding entries.

   $$30+0=30$$

3. Entry (2,1): subtract the corresponding entries.

   $$0-30=-30$$

4. Place the calculated entries in their original row and column positions.

   $$\left[\begin{array}{c}30\\ -30\end{array}\right]$$

5. The first component multiplies î, the second multiplies ĵ.

   $$30\times î-30\times ĵ$$

Answer

The final answer is shown below.