Question
Download Solution PDFA (2, -3, 3), B (5, -3, -4) और C (2, -3, -2) शीर्षों वाले एक त्रिभुज का केन्द्रक कौन-सा बिन्दु है?
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Detailed Solution
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यदि A (x1, y1, z1), B (x2, y2, z2) और C (x3, y3, z3) ΔABC के शीर्ष हैं तो ΔABC का केंद्रक निम्न द्वारा दिया जाता है: \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3},\frac{{{z_1} + {z_2} + {z_3}}}{3}} \right)\)
गणना:
दिया हुआ: ΔABC के शीर्ष हैं: A(2, -3, 3), B(5, -3, -4) और C(2, -3, -2)
जैसा कि हम जानते हैं कि, यदि A (x1, y1, z1), B (x2, y2, z2) और C (x3, y3, z3) ΔABC के शीर्ष हैं तो ΔABC का केंद्रक निम्न द्वारा दिया जाता है: \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3},\frac{{{z_1} + {z_2} + {z_3}}}{3}} \right)\)
\(\Rightarrow \;\left( {\frac{{2 + 5 + 2}}{3},\frac{{ - \;3 - 3 - 3}}{3},\frac{{3 - 4 - 2}}{3}} \right) = \left( {3,\; - 3,\; - 1} \right)\)Last updated on Jun 18, 2025
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