Given vectors vec{a} = 2 hat{i} - hat{j} + 2 | vedclass

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Question

(A) First,calculate the sum of the vectors: $\vec{a} + \vec{b} = (2 \hat{i} - \hat{j} + 2 \hat{k}) + (-\hat{i} + \hat{j} - \hat{k}) = (2-1) \hat{i} +

Vedclass · Accepted Answer

$\hat{i} + \hat{k}$

Vedclass · Answer

(A) First,calculate the sum of the vectors: $\vec{a} + \vec{b} = (2 \hat{i} - \hat{j} + 2 \hat{k}) + (-\hat{i} + \hat{j} - \hat{k}) = (2-1) \hat{i} + (-1+1) \hat{j} + (2-1) \hat{k} = \hat{i} + \hat{k}$.Next,find the magnitude of the resultant vector: $|\vec{a} + \vec{b}| = \sqrt{1^2 + 0^2 + 1^2} = \sqrt{1+1} = \sqrt{2}$.The unit vector in the direction of $\vec{a} + \vec{b}$ is $\hat{u} = \frac{\vec{a} + \vec{b}}{|\vec{a} + \vec{b}|} = \frac{\hat{i} + \hat{k}}{\sqrt{2}}$.The required vector with magnitude $\sqrt{2}$ is $\sqrt{2} 	imes \hat{u} = \sqrt{2} 	imes \frac{\hat{i} + \hat{k}}{\sqrt{2}} = \hat{i} + \hat{k}$.Thus,the correct option is $A$.

Given vectors $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$. The vector in the direction of $\vec{a} + \vec{b}$ with magnitude $\sqrt{2}$ is . . . . . . .

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