Clover 5105. An interactive plot of 3D vectors. Live interior 3d. See how two vectors are related to their resultant, difference and cross product.
Install a good text editor and vector program. Familiarize yourself with Objective-C. Create a development account. Create a new project in Xcode. Create a storyboard for your project. Sketch 3.4.2 Vector Drawing Application. Download was added 6 years ago in the Software download category. Use a VPN Service to download anonymously.
Sketch 2 4 2 – Vector Drawing Application Download
The demo above allows you to enter up to three vectors in the form (x,y,z). Clicking the draw button will then display the vectors on the diagram (the scaleof the diagram will automatically adjust to fit the magnitude of the vectors). You can drag the diagram around and zoom in or out by scrolling with the mouse. Clicking on the end of a vector will also reveal its individual components.
The demo also has the ability to plot 3 other vectors which can be computed from the first two input vectors. The first of these is the resultant, and this is obtained whenthe components of each vector are added together. If the resultant is ( textbf{c} ), then
[ textbf{c} = textbf{a} + textbf{b} ][ left( begin{array}{c}c_x c_y c_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)+left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x + b_x a_y + b_y a_z + b_zend{array}right)]Flinto 1 6 3. In a similar fashion, the difference is what you obtain when you subtract one vector from the other, in this case ( textbf{d} ),
[ textbf{d} = textbf{a} - textbf{b} ][ left( begin{array}{c}d_x d_y d_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)-left(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_x - b_x a_y - b_y a_z - b_zend{array}right)]Sketch 2 4 2 – Vector Drawing Application Free
Finally, the vector product (also known as cross product) is defined as
[ textbf{e} = textbf{a} times textbf{b} = lvert a rvert lvert b rvert sin(theta)hat{n} ][ left( begin{array}{c}e_x e_y e_z end{array} right) =left(begin{array}{c}a_x a_y a_zend{array} right)timesleft(begin{array}{c}b_x b_y b_zend{array}right)=left(begin{array}{c}a_yb_z - a_zb_y a_zb_x - a_xb_za_xb_y - a_yb_xend{array}right)]Geometrically speaking, the cross product's length is equal to the product of the magnitudes of ( textbf{a} ) and ( textbf{b} ) multiplied by the sine of the angle between them. It points in the direction of ( hat{n} ), which is the vector pointing directly out of the plane which ( textbf{a} ) and ( textbf{b} ) lie in. This means that if two vectors point in the same (or exactly opposite) direction, then their cross product will be zero. Try it out above!
Credits
- Thank you to user https://github.com/harshaxnim for creating the ability to add additional vectors, as well as implementing other improvements to this demo's code
