What vector must be added to the two vectors | vedclass

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(B) Let the required vector be $\vec{R}$.According to the problem,the sum of the given vectors and $\vec{R}$ is equal to the unit vector along the $X$

Vedclass · Accepted Answer

$-2\hat{i} + \hat{j} - \hat{k}$

Vedclass · Answer

(B) Let the required vector be $\vec{R}$.According to the problem,the sum of the given vectors and $\vec{R}$ is equal to the unit vector along the $X$-axis,which is $\hat{i}$.$(\hat{i} - 2\hat{j} + 2\hat{k}) + (2\hat{i} + \hat{j} - \hat{k}) + \vec{R} = \hat{i}$Combine the given vectors:$(1+2)\hat{i} + (-2+1)\hat{j} + (2-1)\hat{k} + \vec{R} = \hat{i}$$3\hat{i} - \hat{j} + \hat{k} + \vec{R} = \hat{i}$Now,solve for $\vec{R}$:$\vec{R} = \hat{i} - (3\hat{i} - \hat{j} + \hat{k})$$\vec{R} = \hat{i} - 3\hat{i} + \hat{j} - \hat{k}$$\vec{R} = -2\hat{i} + \hat{j} - \hat{k}$

What vector must be added to the two vectors $\hat{i} - 2\hat{j} + 2\hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$ so that the resultant may be a unit vector along the $X$-axis?

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