Given that a=2b:
\2\hat{i} + m\hat{j} - n\hat{k} = 2(l\hat{i} - 3\hat{j} + 4\hat{k})$\$2\hat{i} + m\hat{j} - n\hat{k} = 2l\hat{i} - 6\hat{j} + 8\hat{k}$ Comparing the coefficients of $\hat{i}, \hat{j},$ and $\hat{k}$: * **$\hat{i}$:** \$2 = 2l \implies l = 1$ * **$\hat{j}$:** $m = -6$ * **$\hat{k}$:** $-n = 8 \implies n = -8$ Substitute these values into the required expression: $\$14l + m + n = 14(1) + (-6) + (-8) = 14 - 14 = 0