Given that A_1+A_2=5 A_3 and A_1-A_2=3 A_3, w | vedclass

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(A) Given equations are:$A_1+A_2=5 A_3$  ---$(i)$$A_1-A_2=3 A_3$  ---(ii)Adding equations $(i)$ and (ii):$2 A_1 = 8 A_3 \Rightarrow A_1 = 4 A_3$Since

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$4$

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(A) Given equations are:$A_1+A_2=5 A_3$  ---$(i)$$A_1-A_2=3 A_3$  ---(ii)Adding equations $(i)$ and (ii):$2 A_1 = 8 A_3 \Rightarrow A_1 = 4 A_3$Since $A_3 = 2 \hat{i} + 4 \hat{j}$, we have $A_1 = 4(2 \hat{i} + 4 \hat{j}) = 8 \hat{i} + 16 \hat{j}$.Subtracting equation (ii) from $(i)$:$2 A_2 = 2 A_3 \Rightarrow A_2 = A_3 = 2 \hat{i} + 4 \hat{j}$.Now, calculating the ratio of magnitudes:$\frac{|A_1|}{|A_2|} = \frac{|8 \hat{i} + 16 \hat{j}|}{|2 \hat{i} + 4 \hat{j}|} = \frac{\sqrt{8^2 + 16^2}}{\sqrt{2^2 + 4^2}}$$= \frac{\sqrt{64 + 256}}{\sqrt{4 + 16}} = \frac{\sqrt{320}}{\sqrt{20}} = \sqrt{\frac{320}{20}} = \sqrt{16} = 4$.

Given that $A_1+A_2=5 A_3$ and $A_1-A_2=3 A_3$, where $A_3=2 \hat{i}+4 \hat{j}$, find the value of $\frac{|A_1|}{|A_2|}$.

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