Mathematics 10 — Exercise 6.1 · Q11 opposite direction

Full question

Find a vector twice as long as 3î−5ĵ in the opposite direction.

Step-by-step solution

1. Multiply every matrix entry by the scalar.

   $$(-2,\left[\begin{array}{c}3\\ -5\end{array}\right])$$

2. Entry (1,1): multiply its value by the scalar.

   $$\left(-2\right)\times 3=-6$$

3. Entry (2,1): multiply its value by the scalar.

   $$\left(-2\right)\times \left(-5\right)=10$$

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

   $$\left[\begin{array}{c}-6\\ 10\end{array}\right]$$

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

   $$-6\times î+10\times ĵ$$

Answer

The final answer is shown below.