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AP EAMCET Engineering 23 Apr 2019 Shift 1 Paper
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Section:
Mathematics
© examsiri.com
Question :
29 of 160
Marks:
+1
,
-0
If α, β , γ are distant real numbers and α + β + γ ≠ 0 , then the points with position vectors α
^
i
+ β
^
j
+ γ
^
k
, β
^
i
+ γ
^
j
+ α
^
k
and γ
^
i
+ α
^
j
+ β
^
k
collinear
vertices of a scalene triangle
vertices of an isosceles triangle
vertices of an equilateral triangle
Validate
Solution:
Let,
O
A
=
α
^
i
+
β
^
j
+
γ
^
k
O
B
=
β
^
i
+
γ
^
j
+
α
^
k
O
C
=
γ
^
i
+
α
^
j
+
β
^
k
So,
A
B
=
(
β
−
α
)
^
i
+
(
γ
−
β
)
^
j
+
(
α
−
γ
)
^
k
B
C
=
(
γ
−
β
)
^
i
+
(
α
−
γ
)
^
j
+
(
β
−
α
)
^
k
C
A
=
(
α
−
γ
)
^
i
+
(
β
−
α
)
^
j
+
(
γ
−
β
)
^
k
This implies,
|
A
B
|
=
√
(
α
−
β
)
2
+
(
β
−
γ
)
2
+
(
γ
−
α
)
2
And,
|
B
C
|
=
√
(
β
−
γ
)
2
+
(
γ
−
α
)
2
+
(
α
−
β
)
2
And
|
C
A
|
=
√
(
γ
−
α
)
2
+
(
α
−
β
)
2
+
(
β
−
γ
)
2
This implies,
|
A
B
|
=
|
B
C
|
=
|
C
A
|
=
√
(
α
−
β
)
2
+
(
β
−
γ
)
2
+
(
γ
−
α
)
2
So, the given position vectors are the vertices of equilateral triangle.
© examsiri.com
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