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प्रश्न
lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is ______.
पर्याय
`-(3a^2)/2`
`(3a^2)/2`
`a^2/3`
`-a^2/3`
MCQ
रिकाम्या जागा भरा
उत्तर
lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is `underlinebb(-(3a^2)/2)`.
Explanation:
`bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)`
= (a) (a) cos 120° + (a) (a) cos 120° + (a) (a) cos 120°
= `a^2 (-1/2) + a^2 (-1/2) + a^2 (-1/2)`
= `-a^2/2 - a^2/2 - a^2/2`
= `-(3a^2)/2`
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