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Question
The vectors 2^i−^j+^k, ^i−3^j−5^k and √3^i−4^j−4^k are the sides of a triangle, which is
The vectors 2^i−^j+^k, ^i−3^j−5^k and √3^i−4^j−4^k are the sides of a triangle, which is
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Solution
The correct option is B Right-angled and isosceles
−−→AB=2^i−^j+^k,−−→AB.−−→DC=2+3−5=0∴△ABC is right-angled.−−→BC=^i−3^j−5^k,−−→CA=√3^i−4^j−4^k∣∣∣−−→CA∣∣∣=√3+16+16=√35, ∣∣∣−−→BC∣∣∣=√1+9+25=√35∴∣∣∣−−→BC∣∣∣=∣∣∣−−→CA∣∣∣⇒△ABC is isosceles.
−−→AB=2^i−^j+^k,−−→AB.−−→DC=2+3−5=0
∴△ABC is right-angled.
−−→BC=^i−3^j−5^k,−−→CA=√3^i−4^j−4^k
∣∣∣−−→CA∣∣∣=√3+16+16=√35,
∣∣∣−−→BC∣∣∣=√1+9+25=√35
∴∣∣∣−−→BC∣∣∣=∣∣∣−−→CA∣∣∣⇒△ABC is isosceles.
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