Three vectors are expressed as vec{a} = 4hat{ | vedclass

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(A) First,find the sum of the vectors $\vec{R} = \vec{a} + \vec{b} + \vec{c}$.$\vec{R} = (4\hat{i} - \hat{j}) + (-3\hat{i} + 2\hat{j}) + (-\hat{k})$$\

Vedclass · Accepted Answer

$\frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}}$

Vedclass · Answer

(A) First,find the sum of the vectors $\vec{R} = \vec{a} + \vec{b} + \vec{c}$.$\vec{R} = (4\hat{i} - \hat{j}) + (-3\hat{i} + 2\hat{j}) + (-\hat{k})$$\vec{R} = (4 - 3)\hat{i} + (-1 + 2)\hat{j} - \hat{k} = \hat{i} + \hat{j} - \hat{k}$.Next,calculate the magnitude of the resultant vector $\vec{R}$:$|\vec{R}| = \sqrt{(1)^2 + (1)^2 + (-1)^2} = \sqrt{1 + 1 + 1} = \sqrt{3}$.The unit vector $\hat{u}$ along the direction of $\vec{R}$ is given by $\hat{u} = \frac{\vec{R}}{|\vec{R}|}$.$\hat{u} = \frac{\hat{i} + \hat{j} - \hat{k}}{\sqrt{3}}$.

Three vectors are expressed as $\vec{a} = 4\hat{i} - \hat{j}$,$\vec{b} = -3\hat{i} + 2\hat{j}$,and $\vec{c} = -\hat{k}$. The unit vector along the direction of the sum of these vectors is:

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