I am personally one of those learners who are visual, please show the work :)
there are only two quaetions.
(1)Find the angle between the given vectors to the nearest tenth of a degree.
u = <2, -4>, v = <3, -8>
(2)Evaluate the expression:
v ⋅ w
Given the vectors:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
Thank you so much!
there are only two quaetions.
(1)Find the angle between the given vectors to the nearest tenth of a degree.
u = <2, -4>, v = <3, -8>
(2)Evaluate the expression:
v ⋅ w
Given the vectors:
r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>
Thank you so much!
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u ∙ v = 38 , | u | = √ 20 , | v | = 3 √10---> cos Θ = 38 / [ 30√2 ]...{ ≈ 26 ° }
v ∙ w = -12 + 16 + 18
v ∙ w = -12 + 16 + 18
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In the first, cos(theta) equals (A dot B)/(norm A times norm B) Take the dot product of vectors U and V for the numerator and the norm for U is sqrt(2^2+-4^2) = sqrt(20) and V is (3^2*-8^2) = sqrt(73), so denominator is sqrt(1460) Once you solve for that, just take arccos(answer) to figure out what theta is.
In the second, the dot product is equal to (3,-8,-3) dot (-4,-2,-6). This equals (-4*3)+(-2*-8)+(-6*-3) = 22
In the second, the dot product is equal to (3,-8,-3) dot (-4,-2,-6). This equals (-4*3)+(-2*-8)+(-6*-3) = 22