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 )
 Author: kayekitty ID: 176131 Card Set: vectors 2 space Updated: 2012-10-08 00:58:53 Tags: vectors math space Folders: Description: vectors 2 space Show Answers: