If bar{a}=hat{imath}+hat{jmath}+hat{k}, bar{b | vedclass

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(C) Given the equation $l \bar{a} + m \bar{b} + n \bar{c} = \overline{0}$.Substituting the vectors: $l(\hat{\imath} + \hat{\jmath} + \hat{k}) + m(2\ha

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$10, -1, -4$

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(C) Given the equation $l \bar{a} + m \bar{b} + n \bar{c} = \overline{0}$.Substituting the vectors: $l(\hat{\imath} + \hat{\jmath} + \hat{k}) + m(2\hat{\imath} - 2\hat{\jmath} + 2\hat{k}) + n(2\hat{\imath} + 3\hat{\jmath} + 2\hat{k}) = 0\hat{\imath} + 0\hat{\jmath} + 0\hat{k}$.Equating the components to zero:$l + 2m + 2n = 0$ $(i)$$l - 2m + 3n = 0$ (ii)$l + 2m + 2n = 0$ (iii)From $(i)$ and (iii),we see they are identical. Subtracting (ii) from $(i)$:$(l + 2m + 2n) - (l - 2m + 3n) = 0$$4m - n = 0 \implies n = 4m$.Substitute $n = 4m$ into $(i)$:$l + 2m + 2(4m) = 0 \implies l + 10m = 0 \implies l = -10m$.Let $m = -1$,then $l = 10$ and $n = -4$.Thus,the values are $(10, -1, -4)$.

If $\bar{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \bar{b}=2 \hat{\imath}-2 \hat{\jmath}+2 \hat{k}, \bar{c}=2 \hat{\imath}+3 \hat{\jmath}+2 \hat{k}$ are three vectors such that $l \bar{a}+m \bar{b}+n \bar{c}=\overline{0}$,then the values of $l, m, n$ are respectively

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