Category: Vector Calculus

Question Number 144783 by nonh1 last updated on 29/Jun/21 Commented by gsk2684 last updated on 29/Jun/21 $$\underset{x\to 0}{\lim }\frac{{\mathrm{x}}^2{\mathrm{x}}^2}{{\mathrm{x}}^2\mathrm{x}+{(\mathrm{x}-\mathrm{x})}^2}$$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{4}}…

Question Number 27 by user1 last updated on 25/Jan/15 $$\mathrm{If}\mathbf{f}=x^{2}z\mathbf{i}-2y^3{z}^2\mathbf{j}+{xy}^{2}z\mathbf{k}.\mathrm{Find}div\mathbf{f},curl\mathbf{f},$$$$at(1,-1,1).$$ Answered by user1 last updated on 03/Nov/14…

Question Number 2 by user1 last updated on 25/Jan/15 $$\mathrm{Find}\mathrm{grad}log\mid \mathbf{r}\mid .$$ Answered by user1 last updated on 29/Oct/14 $$\mathrm{We}\mathrm{have}r=\sqrt{(x^2+y^2+z^2)}$$$$\mathrm{log}\:\mid\boldsymbol{\mathrm{r}}\mid=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\left({x}^{\mathrm{2}}…

Question Number 76302 by john santuy last updated on 26/Dec/19 $$givenvektora=(3,x,-2)$$$$b=(-6,-2,y).whatthevaluex$$$$andyifaandbareparallel?$$ Answered by benjo last updated on 26/Dec/19 $$\mathrm{a}×\mathrm{b}\:=\mathrm{0}…

Question Number 75101 by Rio Michael last updated on 07/Dec/19 $$thevectorequationsoftwolines{L}_{1}and{L}_{2}isgivenby$$$$L_1:r=\mathit{i}-\mathit{j}+3\mathit{k}+\lambda (\mathit{i}-\mathit{j}+\mathit{k})$$$$L_2:r=2\mathit{i}+a\mathit{j}+6\mathit{k}+\mu (2\mathit{i}+\mathit{j}+3\mathit{k})$$$$wherea,\lambda ,\mu arerealconstants.$$$${given}\:{that}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} \:{intersect}\:{find}…