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Mathematics
Mathematics
Problem
Let
A
≡
(
3
,
2
)
A \equiv (3, 2)
A
≡
(
3
,
2
)
and
B
≡
(
5
,
1
)
B \equiv (5, 1)
B
≡
(
5
,
1
)
. ABP is an equilateral triangle constructed on the side of AB remote from the origin then the orthocentre of triangle ABP is: (a)
(
4
−
1
2
3
,
3
2
−
3
)
\left(4 - \frac{1}{2}\sqrt{3}, \frac{3}{2} - \sqrt{3}\right)
(
4
−
2
1
3
,
2
3
−
3
)
(b)
(
4
+
1
2
3
,
3
2
+
3
)
\left(4 + \frac{1}{2}\sqrt{3}, \frac{3}{2} + \sqrt{3}\right)
(
4
+
2
1
3
,
2
3
+
3
)
(c)
(
4
−
1
6
3
,
3
2
−
1
3
3
)
\left(4 - \frac{1}{6}\sqrt{3}, \frac{3}{2} - \frac{1}{3}\sqrt{3}\right)
(
4
−
6
1
3
,
2
3
−
3
1
3
)
(d)
(
4
+
1
6
3
,
3
2
+
1
3
3
)
\left(4 + \frac{1}{6}\sqrt{3}, \frac{3}{2} + \frac{1}{3}\sqrt{3}\right)
(
4
+
6
1
3
,
2
3
+
3
1
3
)
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