Consider vector \(\vec{B} = (3x^2z + y^2)\vec{a_x} + 2xy\vec{a_y} + x^3\vec{a_z}\) Find: a) \(\nabla \cdot \vec{B}\) (10) b) \(\nabla \times \vec{B}\) (10) c) \(\nabla(\nabla \cdot \vec{B})\) (10) d) Is \(\vec{B}\) a conservative vector. Why or why not? (5)
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3: There is no 7.3 in the given vector B, so the answer is not applicable. b) 16: There is no 16 in the given vector B, so the answer is not applicable. c) V3: There is no V3 in the given vector B, so the answer is not applicable. d) 10: There is no 10 in the Show more…
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In each case, find the $x$ - and $v$ -components of vector $\vec{A} :$(a) $A=5.0 \hat{\imath}-6.3 \hat{J} ;($ b) $A=11.2 \hat{j}-9.91 \hat{i} ;(c) A=-15.0 \hat{\imath}+$ $22.4 \hat{j} ;(\mathrm{d}) A=5.0 B,$ where $B=4 \hat{\imath}-6 \hat{j}$
In each case, find the $x$- and $y$-components of vector $\overrightarrow{A}$: (a) $\overrightarrow{A}$ = 5.0$\hat{\imath}$ $-$ 6.3$\hat{\jmath}$; (b) $\overrightarrow{A}$ = 11.2$\hat{\jmath}$ $-$ 9.91$\hat{\imath}$; (c) $\overrightarrow{A}$ = $-$15.0$\hat{\imath}$ $+$ 22.4$\hat{\jmath}$ ; (d) $\overrightarrow{A}$ = 5.0$\overrightarrow{B}$, where $\overrightarrow{B}$ = 4$\hat{\imath}$ $+$ 6$\hat{\jmath}$.
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. Find the direction and magnitude of: (i) the vector sum A + B [10.22m, 145.160 ] (ii) the vector difference A - B, [49.56, 1570 ] and (iii) the vector difference B - A. [49.56m, 3370 ]
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