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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

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# Vectors and surfaces

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