- #1
thenewbosco
- 187
- 0
The question reads:
Identify the following surfaces given that k, l, m, n are fixed values and [tex]\hat{u}[/tex] is a fixed unit vector.
a) [tex]|\overrightarrow{r}|=k[/tex]
b) [tex] \hat{r}\cdot \hat u=l[/tex]
c) [tex] \overrightarrow{r} \cdot \hat{u} = m|\overrightarrow{r}|[/tex] for [tex] -1 \leq 1[/tex]
d)[tex]|\overrightarrow{r} - (\overrightarrow{r}\cdot\hat{u})\hat{u}|=n[/tex]
I am to consider the both the variability in magnitude and direction of [tex]\overrightarrow{r}[/tex]
i was just wondering if the following are correct.
for a) it seems pretty obvious that this is a sphere of radius k, and for b) i see that the cosine of the angle of r vector and u hat is a constant so i think this will lead to a cone.
for c) i am not sure since i get the cosine of the angle between r and uhat is ranging between -1 and 1 so the angle is between 0 and pi, but considering the variability in magnitude of r i am not sure what this defines, and for d) i am not sure what to do
any help would be appreciated
Identify the following surfaces given that k, l, m, n are fixed values and [tex]\hat{u}[/tex] is a fixed unit vector.
a) [tex]|\overrightarrow{r}|=k[/tex]
b) [tex] \hat{r}\cdot \hat u=l[/tex]
c) [tex] \overrightarrow{r} \cdot \hat{u} = m|\overrightarrow{r}|[/tex] for [tex] -1 \leq 1[/tex]
d)[tex]|\overrightarrow{r} - (\overrightarrow{r}\cdot\hat{u})\hat{u}|=n[/tex]
I am to consider the both the variability in magnitude and direction of [tex]\overrightarrow{r}[/tex]
i was just wondering if the following are correct.
for a) it seems pretty obvious that this is a sphere of radius k, and for b) i see that the cosine of the angle of r vector and u hat is a constant so i think this will lead to a cone.
for c) i am not sure since i get the cosine of the angle between r and uhat is ranging between -1 and 1 so the angle is between 0 and pi, but considering the variability in magnitude of r i am not sure what this defines, and for d) i am not sure what to do
any help would be appreciated