lo Find the value as b for which the points Collinear
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Step-by-step explanation:
Let A(a,bn,3) B(2,0,−1) C(1,−1,−3)
Given they are collinear
OA=a
i
^
+b
j
^
+3
k
^
OB=2
i
^
−
k
^
OC=
i
^
−
j
^
−3
k
^
AB
=OB−OA=(2−a)
i
^
+(1−b)
j
^
+(−1−3)
k
^
=(2−a)
i
^
−b
j
^
−4
k
^
−−−(1)
BC
=OC−OB=(1−2)
i
^
+(−1+0)
j
^
+(−1+1)
k
^
=−
i
^
−
j
^
−2
k
^
−−−(2)
As given point are collinear so they are parallel
from (1) & (2)
−1
2−a
=
−1
−b
=
−2
−4
−1
2−a
=2
−1
−b
=2∴a=4
2−a=−2
b=2
b=2
−a=−4
a=4
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