If a = hat{i} + 4 hat{j},b = 2 hat{i} - 2 hat | vedclass

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(C) Given vectors are $a = \hat{i} + 4 \hat{j}$,$b = 2 \hat{i} - 2 \hat{j}$,and $c = 5 \hat{i} + 9 \hat{j}$.We test option $C$: $3 a + b$.$3 a + b = 3

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$3 a + b$

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(C) Given vectors are $a = \hat{i} + 4 \hat{j}$,$b = 2 \hat{i} - 2 \hat{j}$,and $c = 5 \hat{i} + 9 \hat{j}$.We test option $C$: $3 a + b$.$3 a + b = 3(\hat{i} + 4 \hat{j}) + (2 \hat{i} - 2 \hat{j})$$= (3 \hat{i} + 12 \hat{j}) + (2 \hat{i} - 2 \hat{j})$$= (3 + 2) \hat{i} + (12 - 2) \hat{j}$$= 5 \hat{i} + 10 \hat{j}$.Wait,checking the calculation again for $c = 5 \hat{i} + 9 \hat{j}$. Let's re-evaluate $3 a + b$ with the provided $b = 2 \hat{i} - 2 \hat{j}$.Actually,let's check $a + 2 b = (\hat{i} + 4 \hat{j}) + 2(2 \hat{i} - 2 \hat{j}) = \hat{i} + 4 \hat{j} + 4 \hat{i} - 4 \hat{j} = 5 \hat{i} + 0 \hat{j}$.Let's check $3 a + b$ again: $3(\hat{i} + 4 \hat{j}) + (2 \hat{i} - 2 \hat{j}) = 3 \hat{i} + 12 \hat{j} + 2 \hat{i} - 2 \hat{j} = 5 \hat{i} + 10 \hat{j}$.Given the options and the target $c = 5 \hat{i} + 9 \hat{j}$,there is a typo in the provided $b$ or $c$. Assuming $b = 2 \hat{i} - 3 \hat{j}$ as per the original solution provided in the prompt:$3 a + b = 3(\hat{i} + 4 \hat{j}) + (2 \hat{i} - 3 \hat{j}) = 3 \hat{i} + 12 \hat{j} + 2 \hat{i} - 3 \hat{j} = 5 \hat{i} + 9 \hat{j} = c$.

If $a = \hat{i} + 4 \hat{j}$,$b = 2 \hat{i} - 2 \hat{j}$,and $c = 5 \hat{i} + 9 \hat{j}$,then $c$ is equal to:

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