Question
Download Solution PDFप्रारंभिक बिंदु P(2, -3, 4) और अंतिम बिंदु Q(-2, 1, 1) के साथ निर्देशित रेखा खंड द्वारा दर्शाए गए सदिश की लंबाई ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना-
सदिश की लंबाईr \(a\hat{i}+b\hat{j}+c\hat{k}= \sqrt{(a)^{2}+(b)^{2}+(c)^{2}} \)
मान लीजिए सदिश का प्रारंभिक बिंदु A(x1, y1, z1) और अंतिम बिंदु B(x2, y2, z2) है तब
\(|\vec{AB}|=(x_{2}- x_{1})\hat{i}+(y_{2}- y_{1})\hat{i}+(z_{2}- z_{1})\hat{i} \)
गणना-
प्रारंभिक बिंदु P(2,-3,4) और अंतिम बिंदु Q(-2, 1, 1) है
सदिश \(|\vec{PQ}|\) = (-2 - 2)\(\hat{i}\) + (1 - (-3))\(\hat{j}\)+ (1 - 4)\(\hat{k}\)
सदिश \(|\vec{PQ}| \) = -4\(\hat{i}\) + 4\(\hat{j}\) - 3\(\hat{k}\)
अब सदिश की लंबाई \(|\vec{PQ}| \) निम्न द्वारा दी गई है
\(|\vec{PQ}| =\sqrt{(-4)^2+(4)^2+(-3)^2}\)
\(|\vec{PQ}| =\sqrt{16+16+9}\)
\(|\vec{PQ}|= \sqrt{41} \)
∴ सदिश \(|\vec{PQ}| \) की लंबाई\(~ \sqrt{41}\) है
Last updated on Jun 17, 2025
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