Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

image

Play button

image

Play button

image

Progress

1/16

Click to flip

16 Cards in this Set

  • Front
  • Back
What is the right hand rule?
If thumb is z axis, if you close your open palm it goes from the x to the y axis.
What is the distance formula in 3 dimentions?
D = Sqrt[(x{2} - x{1})^2 + (y{2} - y{1})^2 + (z{2} - z{1})^2]
What is the midpoint of two other points in three dimentions?
Midpoint = ( ((x{1}+x{2})/2), ((y{1}+y{2})/2), ((z{1}+z{2})/2) )
What is the equation of a sphere in R^3 with center at (h, k, j) and radius r ?
(x-h)^2 + (y-k)^2 + (z-j)^2 = r^2
What is a vector?
A vector is a quantity that has both magnitude and direction.
What is the zero vector?
A vector whose lenghth is zero that points in any (and all) directions.
How do you do vector addition and subtraction?
Vector addition and subtraction are done by simply doing piecewise addition and subtraction of each of the vectors components two parts.
How do you calculate a scalar times a vector?
A scalar times a vector results in the same vector with each component of the vector multiplied by the scalar.
What is a scalar?
A scalar is not a vector. A scalar is simply a number like 4 or a variable like z.
What is the vector projection of vector b onto vector a?
proj(a)b
How do you calculate the dot product of two vectors?
given vector A and vector B:
A.B = a{1}*b{1} + a{2}*b{2} + a{3}*b{3}
List the properties of dot products
Given vector a, vector b, and vector c:
a.a = |a|^2
a.(b+c)=a.b+a.c
a.b=b.a
(given k scalar)k(a.b)=(ka).b=a.(kb)
a.(the zero vector) = (the number 0, not the vector 0, but the number 0)
What is the geometric interpretation of the dot product?
Given vector a and vector b:
a.b = |a|*|b|*cos(theta)
What is the scalar projection of vector A onto vector B?
Fill in later
What is the Cross Product?
The Cross Product of vector A and B is the resultant vector perpendicular to the plane formed by A and B in the direction of the right hand rule.

AXB = <a{2}b{3} - a{3}b{2}, a{3}b{1} - a{1}b{3}, a{1}b{2} - a{2}b{1}>
List the properties of cross products?
Given vector A, vector B, and vector C:
1)A X B = -(B X A)
2)A X A = 0
3)The vector A X B is orthogonal to both a and B.
-If vector v = A X B, then v.A = 0 & v.B = 0
4)A X (B+C) = A X B + A X C
5)A.(B X C) = scalar triple product = (a X B).C
6)A X (B X C) = vector triple product = (A.C)b-(a.b)C