Question

The question 1B-6?

Answer 1

can you post the question?

Answer 2

is it
what is the locus of points for the equation
\[ \vec{OP} \cdot \textbf{u}= c | \vec{OP}| \]
?

Answer 3

yes, I can't understand: "Then the locus is the nappe of a right circular cone
with axis in the direction u and vertex angle 2θ" How can I reach this conclusion

Answer 4

1B-6 Let O be the origin, c a given number, and u a given direction (i.e., a unit vector).
Describe geometrically the locus of all points P in space that satisfy the vector equation
OP · u = c | OP | .
In particular, tell for what value(s) of c the locus will be (Hint: divide through by | OP | ):
a) a plane
b) a ray (i.e., a half-line)
c) empty

Answer 5

if we divide both sides by |OP| we get
\[ \frac{OP}{|OP|} \cdot u = c \]
that is two unit vectors.
the maximum value of v dot u is 1 when v and u are unit vectors

Answer 6

now consider c=0

any vector OP perpendicular to u , when dotted with u will give 0