If P4,−1,3,Q0,6,7,R−2,1,9 are vertices of a triangle PQR,the equation of the median through R is x−im=y−cs=z−ty, then m+y+s+t+i+c = _____ .(where[.] denotes greatest integer function) and m,s,y are numerically least possible integers.
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a
7
b
12
c
9
d
16
answer is B.
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Detailed Solution
Midpoint of the side PQ is S=4+02,−1+62,3+72=2,52,5The direction ratios of the median RSare2+2,52−1,5−9=4,32,−4=8,3,−8Hence, the equation of the median is x−28=y−523=z−5−8Therefore, m+y+s+t+i+c = 2+52+5+8+3−8=12.5=12