anonymous
  • anonymous
Consider the following vectors. v = 9i + 2j, w = 4i + 3j (a) Find the dot product v·w. v·w = (b) Find the angle between v and w. Give your answer in degrees, and round it to 2 decimal places. Angle between v and w = State whether the vectors are parallel, orthogonal, or neither.
Mathematics
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anonymous
  • anonymous
Consider the following vectors. v = 9i + 2j, w = 4i + 3j (a) Find the dot product v·w. v·w = (b) Find the angle between v and w. Give your answer in degrees, and round it to 2 decimal places. Angle between v and w = State whether the vectors are parallel, orthogonal, or neither.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
dot product = (9 x 4 ) + (2 x 3 ) = 36 +6 =42
anonymous
  • anonymous
length of u = |u| = sqrt ( 9^2 +2^2} = sqrt( 85) |w| = sqrt( 4^2 +3^3) = 5
anonymous
  • anonymous
a . b = |a||b|cos(A) where A is the angle between them

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anonymous
  • anonymous
\[A= \cos^{-1} \frac{a.b}{|a||b|}\]
anonymous
  • anonymous
the rest is calculator work
anonymous
  • anonymous
lol is it orthogonal or parralel or neither?
anonymous
  • anonymous
most likely neither , you have to calculate A
anonymous
  • anonymous
I think its neither
anonymous
  • anonymous
for orthonal A=90degrres, for parallel A=0 and otherwise its nither
anonymous
  • anonymous
keyboard :|
anonymous
  • anonymous
Sweet. It must be neither then.
amistre64
  • amistre64
the slope of the vectors tell you if they are // or L or neither right? 3/4 and 2/9
amistre64
  • amistre64
in R^3 space, the dot is easier to tell the relationship between vectors; but in the plane? y/x is the slope of a vector :)

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