Find a vector of magnitude 5 units,and parall | vedclass

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(A) Given vectors are $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}$.Let $\vec{c}$ be the resultant vector,so $\vec{c}

Vedclass · Accepted Answer

$\pm \frac{3 \sqrt{10}}{2} \hat{i} \pm \frac{\sqrt{10}}{2} \hat{j}$

Vedclass · Answer

(A) Given vectors are $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}$.Let $\vec{c}$ be the resultant vector,so $\vec{c} = \vec{a} + \vec{b}$.$\vec{c} = (2+1) \hat{i} + (3-2) \hat{j} + (-1+1) \hat{k} = 3 \hat{i} + \hat{j}$.The magnitude of $\vec{c}$ is $|\vec{c}| = \sqrt{3^2 + 1^2} = \sqrt{9+1} = \sqrt{10}$.The unit vector in the direction of $\vec{c}$ is $\hat{c} = \frac{\vec{c}}{|\vec{c}|} = \frac{3 \hat{i} + \hat{j}}{\sqrt{10}}$.$A$ vector of magnitude $5$ units parallel to $\vec{c}$ is given by $\pm 5 \hat{c}$.$\pm 5 \left( \frac{3 \hat{i} + \hat{j}}{\sqrt{10}} \right) = \pm \frac{5}{\sqrt{10}} (3 \hat{i} + \hat{j}) = \pm \frac{5 \sqrt{10}}{10} (3 \hat{i} + \hat{j}) = \pm \frac{\sqrt{10}}{2} (3 \hat{i} + \hat{j}) = \pm \frac{3 \sqrt{10}}{2} \hat{i} \pm \frac{\sqrt{10}}{2} \hat{j}$.

Find a vector of magnitude $5$ units,and parallel to the resultant of the vectors $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}.$

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