Question

find the coordinates of the point where the line through the points A(3,1,4) and B(5,1,6)crosses the XY plane​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step 1:
We know that the equation of line passing through the points (x1,y1,z1)
(
x
1
,
y
1
,
z
1
)
and (x2,y2,z2)
(
x
2
,
y
2
,
z
2
)
is
x−x1x2−x1=y−y1y2−y1=z−z1z2−z1
x
−
x
1
x
2
−
x
1
=
y
−
y
1
y
2
−
y
1
=
z
−
z
1
z
2
−
z
1
The line passing through the points (5,1,6)
(
5
,
1
,
6
)
and (3,4,1)
(
3
,
4
,
1
)
is given by,
Substituting for (x1,y1,z1)
(
x
1
,
y
1
,
z
1
)
and (x2,y2,z2)
(
x
2
,
y
2
,
z
2
)
x−53−5=y−14−1=z−61−6
x
−
5
3
−
5
=
y
−
1
4
−
1
=
z
−
6
1
−
6
(i.e) x−5−2=y−13=z−6−5
x
−
5
−
2
=
y
−
1
3
=
z
−
6
−
5
Step 2:
Let this be equal to k
k
x−5−2=y−13=z−6−5=
x
−
5
−
2
=
y
−
1
3
=
z
−
6
−
5
=
k
k
Therefore x=5−2k
x
=
5
−
2
k
y=3k+1
y
=
3
k
+
1
z=6−5k
z
=
6
−
5
k
Let the coordinates of this point be (5−2k,3k+1,6−5k)
(
5
−
2
k
,
3
k
+
1
,
6
−
5
k
)
Step 3:
The equation of YZ
Y
Z
plane,x=0
x
=
0
Since the line passes through the YZ
Y
Z
plane.
5−2k=0
5
−
2
k
=
0
⇒k=52
⇒
k
=
5
2
Step 4:
Now substituting for k
k
we get the coordinates as
(5−2.52,
(
5
−
2.
5
2
,
3.52
3.
5
2
+1,6−5.52)
+
1
,
6
−
5.
5
2
)
On simplifying we get
(0,172
(
0
,
17
2
,−132)