prove by vector method angle in a sphere is right angle
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Answer:
a right angle by vector method.
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ANSWER
To prove: ∠APB=90
0
AB
is the diameter and
O
is the centre
By the law of triangle of vectors:
PA
=
PO
+
OA
PB
=
PO
+
OB
=
PO
−
OA
(∵
OA
=−
OB
)
PA
.
PB
=(
PO
+
OA
).(
PO
−
OA
)
=
∣
∣
∣
∣
PO
∣
∣
∣
∣
2
−
∣
∣
∣
∣
OA
∣
∣
∣
∣
2
(∵
∣
∣
∣
∣
PO
∣
∣
∣
∣
=
∣
∣
∣
∣
OA
∣
∣
∣
∣
=radius)
∴
PA
.
PB
=0
Dot product of
PA
and
PB
=0
∴
PA
⊥
PB
Hence, ∠APB=90
0
solution
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