Question 11(a)
Consider the vectors ∼a=3∼i+2∼j and ∼b=−∼i+4∼j
i. Find 2∼a−∼b .
ii. Find ∼a⋅∼b .
Solution
In this question, we have two vectors which have been written in component form. In part (i), we can individually apply scalar multiplication and perform addition the vector components to obtain the result
2∼a−∼b2∼a−∼b2∼a−∼b2∼a−∼b=2(3∼i+2∼j)−(−∼i+4∼j)=6∼i+4∼j+∼i−4∼j=(6+1)∼i+(4−4)∼j=7∼i
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