vectors 2 space

Card Set Information

Author:
kayekitty
ID:
176131
Filename:
vectors 2 space
Updated:
2012-10-07 20:58:53
Tags:
vectors math space
Folders:

Description:
vectors 2 space
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user kayekitty on FreezingBlue Flashcards. What would you like to do?


  1. geometric vector
    directed line segment
  2. how is bearing different from trig angles?
    • bearing north = 0, goes clockwise
    • trig east = 0, goes counterclockwise
  3. two ways to subtract a - b
    • either tail to tail
    • or a + (-b)
  4. what's an easy way to add vectors ab + bc?
    like matrices, cross out b, answer = ac
  5. if v is a vector, what is kv?
    • also a vector
    • if k > 0, same direction
    • if k = 0, 0 vector
    • if k < 0, opposite direction
    • |kv| = |k||v|
  6. collinear vectors
    vectors that are scalar multiples of one another
  7. how do you find a linear combination when given two vectors?
    • as long as a and b are not collinear
    • if given a and b to find c
    • c = ka + mb
    • write in cartesian form then use system of equations
  8. how do you convert from two points to vector?
    head - tail, x and y coordinates
  9. how to find magnitude of vector a?
    |a| = sqrt(a12 + a22 )
  10. how do you determine if two vectors are collinear?
    if they can become one another by dividing/multiplying by scalar
  11. how to find a vector with magnitude 1 when given vector a?
    • |ka| = |k||a|
    • |k||a| = 1
    • |k|| sqroot formula| = 1
    • k = 1/sqroot formula
    • then multiply k with a
  12. word problems two solutions
    • geometric, use cosine law
    • cartesian, use pythagorean theorem to find angle and convert to cartesian vectors
  13. if using trig what must you always do?
    • convert bearing angle to trig angle
    • trig angle = 450 - bearing angle
  14. how to convert to component form? for vector a
    = [magnitude*cos degree, magnitude *sin degree]
  15. equilibrant
    force that counterbalances resultant, equal in mag. opposite in direction
  16. two methods for forces
    • use sine law with magnitude resultant/sin angle when asked to find the magnitudes of two ropes
    • pay attention to F and C patterns
    • cartesian method: use magnitudes and variables to represent the t1 and t2 then use substitution method and system of equations
  17. two formulas for dot product
    • a * b = |a||b|costheta
    • a * b = a1b1 + a2b2
  18. what does the dot product give and reveal?
    • dot product = scalar
    • if dot product greater than 0, = acute angle
    • dot product smaller than 0, obtuse
    • if = 0, 90 degree angle
  19. to find the angle using dot product, what formula?
    a1b1 + a2b2 = |a||b|costheta
  20. properties o dot product
    • a * a = |a|2
    • a * 0(vector) = 0(scalar)
    • |a+b|2 = |a|2   + 2a * b + |b|2
    • |a+b|2 = (a+b)*(a+b)
    • a * u = |a| if u is unit vector w/ same direction as a
    • be careful when simplifying write out with x and y
  21. if in a triangle there are the same dot product for angles what does it mean?
    the angles are the same!
  22. what is the formula for projects? (2)
    • if a on b
    • O = (a*b)/(b*b)
    • O = (a*b)/(|b|2 )

What would you like to do?

Home > Flashcards > Print Preview