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ethanyayger
08.09.2020 •
Mathematics
Let L be the line with parametric equations x=5+t,y=6,z=−2−3t. Find the vector equation for a line that passes through the point P=(−5,7,−8) and intersects L at a point that is distance 3 from the point Q=(5,6,−2). Note that there are two possible correct answers. Use the square root symbol √ where needed to give an exact value for your answer.
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Ответ:
The required equations are
Step-by-step explanation:
The given parametric equation of the line,
, is
so, an arbitrary point on the line is ![R(x,y,z)=R(5+t, 6, -2-3t)](/tpl/images/0745/6500/54eb0.png)
The vector equation of the line passing through the points
and
is
The given equation can also be written as
The standard equation of the line passes through the point
and having direction
is
Here, The value of the parameter,
, of any point
at a distance
from the point,
, can be determined by
Comparing equations
and ![(iii)](/tpl/images/0745/6500/59442.png)
The line is passing through the point
having direction
.
Note that the point
is the same as
obtained above.
Now, the value of the parameter,
, for point
at distance
from the point
can be determined by equation
, we have
Put the value of
in equation
, the required equations are as follows:
For![t= \frac {3}{\sqrt {10}}](/tpl/images/0745/6500/d7bc8.png)
and for
,
Ответ:
<3 is a "sideways heart" (love, friendship) or even meaning "broken heart" but some people might think that you have a crush on them but you don't also it depends which situation your in and how you are using it.