Let L be the line that passes through the point x 0 , y 0 , z 0 and is parallel to the vector v = a , b , c , where a , b , and c are nonzero. Show that a point x , y , z lies on the line L if and only if x − x 0 a = y − y 0 b = z − z 0 c These equations, which are called the symmetric equations of L , provide a nonparametric representation of L .
Let L be the line that passes through the point x 0 , y 0 , z 0 and is parallel to the vector v = a , b , c , where a , b , and c are nonzero. Show that a point x , y , z lies on the line L if and only if x − x 0 a = y − y 0 b = z − z 0 c These equations, which are called the symmetric equations of L , provide a nonparametric representation of L .
Let L be the line that passes through the point
x
0
,
y
0
,
z
0
and is parallel to the vector
v
=
a
,
b
,
c
,
where a, b, and c are nonzero. Show that a point
x
,
y
,
z
lies on the line L if and only if
x
−
x
0
a
=
y
−
y
0
b
=
z
−
z
0
c
These equations, which are called the symmetric equations of L, provide a nonparametric representation of L.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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