find the equation the coordinates (2,0) and (0,3)
Answers
Answer:
Answer
The equation of a line passing through two points A(x
1
,y
1
,z
1
)
and B(x
2
,y
2
,z
2
) is
x
2
−x
1
x−x
1
=
y
2
−y
1
y−y
1
=
z
2
−z
1
z−z
1
Given the lines passes through the points
A(2,-3,1)
∴x
1
=2,y
1
=−3,z
1
=1
B(3,-4,-5)
∴x
2
=3,y
2
=−4,z
2
=−5
So, the equation of line is
3−2
x−2
=
−4+3
y+3
=
−5−1
z−1
so,
1
x−2
=
−1
y+3
=
−6
z−1
=k
x=k+2
y=−k+3
z=−6k+1
Let (x,y,z) be the coordinates of the point where the line crosses the plane 2x+y+z=7
Putting values of x,y,z from the equation (1) in the plane,
2x+y+z=7
2(k+2)+(−k+3)+(−6k+1)=7
2k+4−k+3−6k+1=7
−5k+8=7
5k=8−7
5k=1
∴k=
5
1
putting value of k in x,y,z
x=k+2=
5
1
+2=
5
11
y=−k+3=−
5
1
+3=
5
14
z=−6k+1=
5
−6
+1=
5
−1
therefore, the coordinates of the given points are(
5
11
,
5
14
,
5
−1
)
Step-by-step explanation:
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