The points with position vectors (6000i + 300j), (40001 - 800]), and (ai - 52001) are collinear if:
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Explanation:
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Show that the points whose position vectors are as given below are collinear:
2
i
^
+
j
^
−
k
^
,3
i
^
−2
j
^
+
k
^
and
i
^
+4
j
^
−3
k
^
November 22, 2019avatar
Chaahat Malik
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ANSWER
3 points A,B,C are collinear if
∣
∣
∣
∣
AB
∣
∣
∣
∣
+
∣
∣
∣
∣
BC
∣
∣
∣
∣
=
∣
∣
∣
∣
AC
∣
∣
∣
∣
AB
=
OB
−
OA
=3
i
^
−2
j
^
+
k
^
−2
i
^
−
j
^
+
k
^
=
i
^
−3
j
^
+2
k
^
∣
∣
∣
∣
AB
∣
∣
∣
∣
=
(1)
2
+(−3)
2
+(2)
2
=
1+9+4
=
14
units.
BC
=
OC
−
OB
=
i
^
+4
j
^
−3
k
^
−3
i
^
+2
j
^
−
k
^
=−2
i
^
+6
j
^
−4
k
^
∣
∣
∣
∣
BC
∣
∣
∣
∣
=
(−2)
2
+(6)
2
+(−4)
2
=
4+36+16
=
56
=2
14
units.
AC
=
OC
−
OA
=
i
^
+4
j
^
−3
k
^
−2
i
^
−
j
^
+
k
^
=−
i
^
+3
j
^
−2
k
^
∣
∣
∣
∣
AC
∣
∣
∣
∣
=
(−1)
2
+(3)
2
+(−2)
2
=
1+9+4
=
14
units.
∴
∣
∣
∣
∣
AB
∣
∣
∣
∣
+
∣
∣
∣
∣
AC
∣
∣
∣
∣
=
∣
∣
∣
∣
BC
∣
∣
∣
∣
Hence B,A and C are collinear.