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Question
In a right-angled triangle ABC, if the hypotenuse AB = p, then what is −−→AB.−−→AC+−−→BC.−−→BA+−−→CA.−−→CB equal to?
In a right-angled triangle ABC, if the hypotenuse AB = p, then what is −−→AB.−−→AC+−−→BC.−−→BA+−−→CA.−−→CB equal to?
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Solution
The correct option is B p2
−−→AB.−−→AC+−−→BC.−−→BA+−−→CA.−−→CB=−−→AB.−−→AC−−−→BC.−−→AB+0 ...(−−→CA⊥−−→CB)=−−→AB.−−→AC+−−→CB.−−→AB=−−→AB.(−−→AC+−−→CB)=−−→AB.(−−→AB)=|−−→AB|2=p2
Answer is option (B)
−−→AB.−−→AC+−−→BC.−−→BA+−−→CA.−−→CB
=−−→AB.−−→AC−−−→BC.−−→AB+0 ...(−−→CA⊥−−→CB)
=−−→AB.−−→AC+−−→CB.−−→AB
=−−→AB.(−−→AC+−−→CB)
=−−→AB.(−−→AB)
=|−−→AB|2
=p2
Answer is option (B)
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