Question 105: Motion in 2D & Vectors

Question

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 sum of these vectors is

Accepted Answer

$$ \begin{aligned} \vec{r} & =\vec{a}+\vec{b}+\vec{c}=4 \hat{i}-\hat{j}-3 \hat{i}+2 \hat{j}-\hat{k} \ & =\hat{i}+\hat{j}-\hat{k} \ \hat{r} & =\frac{\vec{r}}{|r|}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{1^2+1^2+(-1)^2}}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}} \end{aligned} $$

Answer

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

Answer

$\quad \frac{1}{3}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$

Answer

$\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$

Answer

$\frac{1}{\sqrt{2}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$

Motion in 2D & Vectors

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 sum of these vectors is

Choose the correct answer: