Find the sum of the vectors vec{a}=hat{i}-2 h | vedclass

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(A) Given vectors are $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.The sum o

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$-4\hat{j}-\hat{k}$

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(A) Given vectors are $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.The sum of the vectors is given by $\vec{a} + \vec{b} + \vec{c} = (\vec{a}_x + \vec{b}_x + \vec{c}_x)\hat{i} + (\vec{a}_y + \vec{b}_y + \vec{c}_y)\hat{j} + (\vec{a}_z + \vec{b}_z + \vec{c}_z)\hat{k}$.Substituting the components:$\vec{a} + \vec{b} + \vec{c} = (1 - 2 + 1)\hat{i} + (-2 + 4 - 6)\hat{j} + (1 + 5 - 7)\hat{k}$.Calculating the coefficients:$x$-component: $1 - 2 + 1 = 0$.$y$-component: $-2 + 4 - 6 = -4$.$z$-component: $1 + 5 - 7 = -1$.Thus,the sum is $0\hat{i} - 4\hat{j} - 1\hat{k} = -4\hat{j} - \hat{k}$.

Find the sum of the vectors $\vec{a}=\hat{i}-2 \hat{j}+\hat{k}$,$\vec{b}=-2 \hat{i}+4 \hat{j}+5 \hat{k}$,and $\vec{c}=\hat{i}-6 \hat{j}-7 \hat{k}$.

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