InterviewSolution
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InterviewSolution
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If `A(x_1, y_1),B(x_2, y_2) ` and `C(x_3,y_3)`are vertices of an equilateral triangle whose each side is equal to `a`, then prove that`|[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4` |
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Answer» Area of an equilateral triangle=`(sqrt3 a^2)/4 ` area= `1/2|(x_1, y_1, 1),(x_2, y_2, 1),(x_3, y_3, 1)|` `sqrt3 a^2/4 = 1/2 |(x_1, y_1,1),(x_2,y_2,1),(x_3,y_3,1)|` `sqrt3 a^2 = 2|(x_1 , y_1, 1),(x_2, y_2, 1),(x_3, y_3,1)|` `sqrt3 a^2 = |(x_1, y_1, 2),(x_2,y_2,2),(x_3,y_3,2)|` `3a^4 = |(x_1, y_1, 2),(x_2,y_2, 2),(x_3,y_3,2)|^2` hence proved |
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