@ The points (3,3), (2, -W & C3,-1) are
Collinear. (True) or (false
Answers
Answered by
7
Answer:
A=(1,−2,−8)
B=(5,0,−2)
C=(11,3,7)
A,B,C are collinear if
∣
∣
∣
∣
AB
∣
∣
∣
∣
+
∣
∣
∣
∣
BC
∣
∣
∣
∣
=
∣
∣
∣
∣
AC
∣
∣
∣
∣
AB
=(5−1)
i
^
+(0+2)
j
^
+(−2+8)
k
^
=4
i
^
+2
j
^
+6
k
^
∣
∣
∣
∣
AB
∣
∣
∣
∣
=
16+4+36
=2
14
BC
=(11−5)
i
^
+(3−0)
j
^
+(7+2)
k
^
=6
i
^
+3
j
^
+9
k
^
∣
∣
∣
∣
BC
∣
∣
∣
∣
=
36+9+81
=3
14
AC
=(11−1)
i
^
+(3+2)
j
^
+(7+8)
k
^
=10
i
^
+5
j
^
+15
k
^
∣
∣
∣
∣
AC
∣
∣
∣
∣
=
100+25+225
=5
14
Thus
∣
∣
∣
∣
AB
∣
∣
∣
∣
+
∣
∣
∣
∣
BC
∣
∣
∣
∣
=
∣
∣
∣
∣
AC
∣
∣
∣
∣
let B divide AC in k:1
then
(5,0,−2)=
k+1
k(11,3,7)+1(1,−2,−8)
=
k+1
(11k+1,3k−2,7k−8)
⇒k=2/3⇒k:1⇒2:3
⇒ B divide AC in 2:3.
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