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MHT CET 2017 Math Solved Paper
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© examsnet.com
Question : 3
Total: 50
If
z
1
and
z
2
are z-coordinates of the points of trisection of the segment joining the points A(2,1,4 ), B (-1,3 ,6 ), then
z
1
+
z
2
=
1
4
5
10
Validate
Solution:
(d) Let P & Q are the points with z-coordinates as
z
1
and
z
2
respectively which trisect the line segment AB.
Then, coordinates of P
=
(
1
×
(
−
1
)
+
2
×
2
1
+
2
,
1
×
3
+
2
×
1
1
+
2
,
1
×
6
+
2
×
4
1
+
2
)
Now, z-coordinate of
P
=
1
×
6
+
2
×
4
1
+
2
i.e.
z
1
=
6
+
8
3
=
14
3
And coordinates of Q
=
(
2
×
(
−
1
)
+
1
×
2
2
+
1
,
2
×
3
+
1
×
1
2
+
1
,
2
×
6
+
1
×
4
2
+
1
)
So,
z
-coordinate of
Q
=
2
×
6
+
1
×
4
2
+
1
i.e.
z
2
=
12
+
4
3
=
16
3
Hence,
z
1
+
z
2
=
14
3
+
16
3
=
30
3
=
10
© examsnet.com
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