Solution Found!
Explain why or why not Determine whether the
Chapter 14, Problem 37E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The vector field \(\mathbf{F}=\left\langle 3 x^{2}, 1\right\rangle\) is a gradient field for both \(\varphi_{1}(x, y)=x^{3}+y \text { and } \varphi_{2}(x, y)=y+x^{3}+100\).
b. The vector field \(\mathbf{F}=\frac{\langle y, x\rangle}{\sqrt{x^{2}+y^{2}}}\) is constant in direction and magnitude on the unit circle.
c. The vector field \(\mathbf{F}=\frac{\langle y, x\rangle}{\sqrt{x^{2}+y^{2}}}\) is neither a radial field nor a rotation field.
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The vector field \(\mathbf{F}=\left\langle 3 x^{2}, 1\right\rangle\) is a gradient field for both \(\varphi_{1}(x, y)=x^{3}+y \text { and } \varphi_{2}(x, y)=y+x^{3}+100\).
b. The vector field \(\mathbf{F}=\frac{\langle y, x\rangle}{\sqrt{x^{2}+y^{2}}}\) is constant in direction and magnitude on the unit circle.
c. The vector field \(\mathbf{F}=\frac{\langle y, x\rangle}{\sqrt{x^{2}+y^{2}}}\) is neither a radial field nor a rotation field.
ANSWER:Solution 37E
Step 1
