assignment Homework
assignment Homework
assignment Homework
Let \begin{align} \boldsymbol{\vec a} &= \boldsymbol{\hat x}-3\boldsymbol{\hat y}-\boldsymbol{\hat z}\\ \boldsymbol{\vec b} &= \boldsymbol{\hat x}+\boldsymbol{\hat y}+2\boldsymbol{\hat z}\\ {\boldsymbol{\vec c}} &= -2\boldsymbol{\hat x}-\boldsymbol{\hat y}+\boldsymbol{\hat z}\\ \boldsymbol{\vec d} &= -\boldsymbol{\hat x}-\boldsymbol{\hat y}+\boldsymbol{\hat z} \end{align}
Which pairs (if any) of these vectors
assignment Homework
assignment Homework
accessibility_new Kinesthetic
10 min.
arms complex numbers Argand diagram complex plane rectangular form exponential form complex conjugate math
Students move their left arm in a circle to trace out the complex plane (Argand diagram). They then explore the rectangular and exponential representations of complex numbers by using their left arm to show given complex numbers on the complex plane. Finally they enact multiplication of complex numbers in exponential form and complex conjugation.assignment Homework
Consider the vector field \(\vec F=(x+2)\hat{x} +(z+2)\hat{z}\).
assignment Homework
Show that the plane polar coordinates we have chosen are equivalent to spherical coordinates if we make the choices:
assignment Homework
Sketch the volume charge density: \begin{equation} \rho (x,y,z)=c\,\delta (x-3) \end{equation}
Use the cross product to find the components of the unit vector \(\mathbf{\boldsymbol{\hat n}}\) perpendicular to the plane shown in the figure below, i.e. the plane joining the points \(\{(1,0,0),(0,1,0),(0,0,1)\}\).