Find the values of x, y and z so that the vec | vedclass

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(A) Two vectors $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$ and $\vec{b} = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k}$ are equal if and only if t

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$x = 2, y = 2, z = 1$

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(A) Two vectors $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$ and $\vec{b} = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k}$ are equal if and only if their corresponding components are equal,i.e.,$a_1 = b_1, a_2 = b_2$ and $a_3 = b_3$.Given vectors are $\vec{a} = x \hat{i} + 2 \hat{j} + z \hat{k}$ and $\vec{b} = 2 \hat{i} + y \hat{j} + \hat{k}$.Comparing the components of $\vec{a}$ and $\vec{b}$:For the $\hat{i}$ component: $x = 2$.For the $\hat{j}$ component: $2 = y$,which means $y = 2$.For the $\hat{k}$ component: $z = 1$.Therefore,the values are $x = 2, y = 2, z = 1$.

Find the values of $x, y$ and $z$ so that the vectors $\vec{a} = x \hat{i} + 2 \hat{j} + z \hat{k}$ and $\vec{b} = 2 \hat{i} + y \hat{j} + \hat{k}$ are equal.

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