2.
If the position vectors of the vertices of a triangle be
2i + 4j-k, 4i + 5j+k and 3i+6j -3k, then the triangle
is
(a) Right angled
(b) Isosceles
(c) Equilateral
(d) Right angled isosceles
Answers
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12th
Maths
Vectors
Operations on Vectors
If the position vectors of ...
MATHS
If the position vectors of the vertices of a triangle be 6i + 4j + 5k, 4i + 5j + 6k and 5i + 6j + 4k then the triangle is
December 26, 2019avatar
Rituparna Sagar
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ANSWER
We have,
Let the vertices of triangle is
OA
=(6
i
+4
j
+5
k
)
OB
=(4
i
+5
j
+6
k
)
OC
=(5
i
+6
j
+4
k
)
Now,
AB
=
OB
−
OA
AB
=(4
i
+5
j
+6
k
)−(6
i
+4
j
+5
k
)
AB
=4
i
+5
j
+6
k
−6
i
−4
j
−5
k
AB
=−2
i
+
j
+
k
BC
=
OC
−
OB
BC
=(5
i
+6
j
+4
k
)−(4
i
+5
j
+6
k
)
BC
=5
i
+6
j
+4
k
−4
i
−5
j
−6
k
BC
=
i
+
j
−2
k
CA
=
OA
−
OC
CA
=(6
i
+4
j
+5
k
)−(5
i
+6
j
+4
k
)
CA
=6
i
+4
j
+5
k
−5
i
−6
j
−4
k
CA
=
i
−2
j
+
k
Now,
∣AB∣=
(−2)
2
+1
2
+1
2
=
6
∣BC∣=
1
2
+1
2
+(−2)
2
=
6
∣CA∣=
1
2
+(−2)
2
+1
2
=
6
Then,
AB=BC=CA=
6
Hence, It triangle is equilateral triangle.