vectors 2 space

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  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 )

Card Set Information

Author:
kayekitty
ID:
176131
Filename:
vectors 2 space
Updated:
2012-10-08 00:58:53
Tags:
vectors math space
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Description:
vectors 2 space
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