About is tangent vector?
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Vector equation for a line is like this $$r(t)=r_0+tv$$
But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$
vectors
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up vote
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Vector equation for a line is like this $$r(t)=r_0+tv$$
But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$
vectors
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Vector equation for a line is like this $$r(t)=r_0+tv$$
But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$
vectors
Vector equation for a line is like this $$r(t)=r_0+tv$$
But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$
vectors
edited Aug 29 at 8:54
gimusi
71.2k73786
71.2k73786
asked Aug 29 at 8:52
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1 Answer
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Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.
Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain
$$tv=4bar t v=bar t (4v)$$
and the two lines with $t,bar t in mathbbR$
- $r(t)=r_0+tv$
- $bar r(t)=r_0+bar t(4v)$
decribe, with different parametrization, the same set of points in $mathbbR^3$.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.
Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain
$$tv=4bar t v=bar t (4v)$$
and the two lines with $t,bar t in mathbbR$
- $r(t)=r_0+tv$
- $bar r(t)=r_0+bar t(4v)$
decribe, with different parametrization, the same set of points in $mathbbR^3$.
add a comment |Â
up vote
0
down vote
Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.
Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain
$$tv=4bar t v=bar t (4v)$$
and the two lines with $t,bar t in mathbbR$
- $r(t)=r_0+tv$
- $bar r(t)=r_0+bar t(4v)$
decribe, with different parametrization, the same set of points in $mathbbR^3$.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.
Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain
$$tv=4bar t v=bar t (4v)$$
and the two lines with $t,bar t in mathbbR$
- $r(t)=r_0+tv$
- $bar r(t)=r_0+bar t(4v)$
decribe, with different parametrization, the same set of points in $mathbbR^3$.
Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.
Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain
$$tv=4bar t v=bar t (4v)$$
and the two lines with $t,bar t in mathbbR$
- $r(t)=r_0+tv$
- $bar r(t)=r_0+bar t(4v)$
decribe, with different parametrization, the same set of points in $mathbbR^3$.
edited Aug 29 at 9:03
answered Aug 29 at 8:53
gimusi
71.2k73786
71.2k73786
add a comment |Â
add a comment |Â
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