Question 11(a)

Cover Image for Question 11(a)

Question 11(a)

Consider the vectors a∼=3i∼+2j∼\underset{\sim}{a} = 3\underset{\sim}{i} + 2\underset{\sim}{j} and b∼=−i∼+4j∼\underset{\sim}{b} = -\underset{\sim}{i} + 4\underset{\sim}{j}

i. Find 2a∼−b∼2\underset{\sim}{a} - \underset{\sim}{b} .

ii. Find a∼⋅b∼\underset{\sim}{a} \cdot \underset{\sim}{b} .

Solution

For part (i) we add the vector components individually

2a∼−b∼=2(3i∼+2j∼)−(−i∼+4j∼)=6i∼+4j∼+i∼−4j∼=(6+1)i∼+(4−4)j∼=7i∼\begin{aligned} & 2\underset{\sim}{a} - \underset{\sim}{b} \\ =& 2\left(3\underset{\sim}{i} + 2\underset{\sim}{j}\right) - \left(-\underset{\sim}{i} + 4\underset{\sim}{j}\right) \\ =& 6\underset{\sim}{i} + 4\underset{\sim}{j} +\underset{\sim}{i} - 4\underset{\sim}{j} \\ =& (6+1)\underset{\sim}{i} + (4-4)\underset{\sim}{j} \\ =& 7\underset{\sim}{i} \\ \end{aligned}

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