दो सदिश फलनों के लिए पर का अवकलज ज्ञात करें।

Question

दो सदिश फलनों

$\mathbf{a}(t)=(t^3-t)\mathbf{i}+(3t+4)\mathbf{j}+2t^2\mathbf{k}\quad\text{}\quad\mathbf{b}(t)=(7-t^2)\mathbf{i}+(4+6t)\mathbf{j}-6t^3\mathbf{k}$ के लिए $t=1$ पर $\mathbf{a}(t)\cdot\mathbf{b}(t)$ का अवकलज ज्ञात करें।

29 Apr 2025

Answer :

Word Count : 305

हमें दो सदिश फलन दिए गए हैं: $$ \mathbf{a}(t) = (t^3 - t)\mathbf{i} + (3t + 4)\mathbf{j} + 2t^2\mathbf{k} $$ $$ \mathbf{b}(t) = (7 - t^2)\mathbf{i} + (4 + 6t)\mathbf{j} - 6t^3\mathbf{k} $$ हमें $\mathbf{a}(t) \cdot \mathbf{b}(t)$ का अवकलज निकालना है और फिर $t = 1$ पर उसका मान ज्ञात करना है। --- ### चरण 1: डॉट प्रोडक्ट करें $$ \mathbf{a}(t) __________ _____ ____ ______ _____ _________.
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