Dot & Cross Product in 3D: Day 4

Question 1

What is the dot product equation for 3D vectors?

Answer 1

a . b=axbx+ayby+azbz

Question 2

What does collinear mean?

Answer 2

parallel vectors

• any multiple of the vector is collinear to the vector
  ex. [3,5,-2] is collinear to [6,10,-4] - multiplied by 2

Question 3

How can you find a vector perpendicular to ex [1,2,3]?

Answer 3

• if perpendicular, the dot product=0
• can plug in any value for [x,y,z]
• many possible answers because you can sub any numbers in for the components*

Question 4

What is the equation of the cross product multiplication?

Answer 4

|a x b|=|a| |b| sinθ

• creates a vector product
• result=0 when vectors are parallel

Question 5

What is the right-hand rule and what does it determine?

Answer 5

• right-hand rule determines the direction of the cross product vector (in or out of the page)
• point fingers in direction of a, curl fingers towards b*

Question 6

What is the equation of the cross product of cartesian vector?

Answer 6

a x b=[aybz-azby, azbx-axbz, axby-aybx]

            x. y.                z.        * write out components twice over b components twice

Question 7

What are the applications of the cross product multiplication?

Answer 7

1) area of a parallelogram - A=|a x b| or A=|b||a| sin θ
2) area of a triangle- A=|a x b| /2
3) torque- T= |r| |f| sin θ (direction from RHR)
4) volume of parallelpiped- v=|a x b . c |