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let-c-is-a-constant-vector-and-r-xi-yj-zk-then-proved-that-grad-c-r-n-n-c-r-n-2-c-r-c-




Question Number 84969 by subhankar10 last updated on 18/Mar/20
let c is a constant vector and r^→ =xi^� +yj^� +zk^�  then proved that grad ∣c×r^→ ∣^n =n∣c×r^→ ∣^(n−2) c×(r^→ ×c).
$$\mathrm{let}\:\mathrm{c}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{vector}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{r}}=\mathrm{x}\hat {\mathrm{i}}+\mathrm{y}\hat {\mathrm{j}}+\mathrm{z}\hat {\mathrm{k}}\:\mathrm{then}\:\mathrm{proved}\:\mathrm{that}\:\mathrm{grad}\:\mid\mathrm{c}×\overset{\rightarrow} {\mathrm{r}}\mid^{\mathrm{n}} =\mathrm{n}\mid\mathrm{c}×\overset{\rightarrow} {\mathrm{r}}\mid^{\mathrm{n}−\mathrm{2}} \mathrm{c}×\left(\overset{\rightarrow} {\mathrm{r}}×\mathrm{c}\right). \\ $$

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