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geometric vector
directed line segment

how is bearing different from trig angles?
 bearing north = 0, goes clockwise
 trig east = 0, goes counterclockwise

two ways to subtract a  b
 either tail to tail
 or a + (b)

what's an easy way to add vectors ab + bc?
like matrices, cross out b, answer = ac

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 = kv

collinear vectors
vectors that are scalar multiples of one another

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

how do you convert from two points to vector?
head  tail, x and y coordinates

how to find magnitude of vector a?
a = sqrt(a1^{2} + a2^{2} )

how do you determine if two vectors are collinear?
if they can become one another by dividing/multiplying by scalar

how to find a vector with magnitude 1 when given vector a?
 ka = ka
 ka = 1
 k sqroot formula = 1
 k = 1/sqroot formula
 then multiply k with a

word problems two solutions
 geometric, use cosine law
 cartesian, use pythagorean theorem to find angle and convert to cartesian vectors

if using trig what must you always do?
 convert bearing angle to trig angle
 trig angle = 450  bearing angle

how to convert to component form? for vector a
= [magnitude*cos degree, magnitude *sin degree]

equilibrant
force that counterbalances resultant, equal in mag. opposite in direction

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

two formulas for dot product
 a * b = abcostheta
 a * b = a1b1 + a2b2

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

to find the angle using dot product, what formula?
a1b1 + a2b2 = abcostheta

properties o dot product
 a * a = a^{2}
 a * 0(vector) = 0(scalar)
 a+b^{2} = a^{2 } + 2a * b + b2
 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

if in a triangle there are the same dot product for angles what does it mean?
the angles are the same!

what is the formula for projects? (2)
 if a on b
 O = (a*b)/(b*b)
 O = (a*b)/(b^{2} )

