MHT CET 2017 Math Solved Paper

(d) Let P & Q are the points with z-coordinates as z1 and z2 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. z1=

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. z2=

12+4

3

=

16

3

Hence,z1+z2=

14

3

+

16

3

=

30

3

=10