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(A) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$.$\vec{R} = \vec{A} + \vec{B} = (-2 \hat{i} + 3 \hat{j} + \ha

Vedclass · Accepted Answer

$\frac{-\hat{i} + 5 \hat{j} - 3 \hat{k}}{\sqrt{35}}$

Vedclass · Answer

(A) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$.$\vec{R} = \vec{A} + \vec{B} = (-2 \hat{i} + 3 \hat{j} + \hat{k}) + (\hat{i} + 2 \hat{j} - 4 \hat{k})$$\vec{R} = (-2 + 1) \hat{i} + (3 + 2) \hat{j} + (1 - 4) \hat{k} = -\hat{i} + 5 \hat{j} - 3 \hat{k}$Now,calculate the magnitude of the resultant vector $\vec{R}$:$|\vec{R}| = \sqrt{(-1)^2 + (5)^2 + (-3)^2} = \sqrt{1 + 25 + 9} = \sqrt{35}$The unit vector $\hat{R}$ in the direction of $\vec{R}$ is given by $\hat{R} = \frac{\vec{R}}{|\vec{R}|}$.$\hat{R} = \frac{-\hat{i} + 5 \hat{j} - 3 \hat{k}}{\sqrt{35}}$Thus,the correct option is $A$.

$A$ unit vector in the direction of the resultant vector of $\vec{A} = -2 \hat{i} + 3 \hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2 \hat{j} - 4 \hat{k}$ is

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