anonymous
  • anonymous
Can someone help me with some math questions? I'll fan and medal. :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
hartnn
  • hartnn
do you know how to get projection of one vector on other? tried to solve this?
hartnn
  • hartnn
Projection of vector a on vector b is \(\LARGE \dfrac{a.b}{|b|}\)

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anonymous
  • anonymous
So it would start off like this?.... (1.6i + 3.3j) (-2.1i -0.5j) = -3.36 -6.93 -1.65 -0.8
hartnn
  • hartnn
note that \(i . j \) and \(j.i\) both = 0 as they are perpendicular vectors!
hartnn
  • hartnn
so you'll only have 1.6*(-2.1) + 3.3*(-0.5) = ...
anonymous
  • anonymous
So just to be clear - Whenever you're multiplying the different variables in a vector, the become zero?
hartnn
  • hartnn
correction* whenever you're taking the dot product of perpendicular vectors, the product = 0 i , j and k are perpendicular vecotrs
anonymous
  • anonymous
Got it. So... 1.6*(-2.1) + 3.3*(-0.5) = -3.36i -1.65j then you divide that answer by (-2.1i -0.5j) (-3.36i -1.65j) / (-2.1i -0.5j) =...
anonymous
  • anonymous
Give me just a second on the division. I think I did something wrong.
hartnn
  • hartnn
so your u.v will be = 1.6*(-2.1) + 3.3*(-0.5) = ... its a numeric value, because its a dot product it won't have i's and j's in it!
hartnn
  • hartnn
and for the denominator its magnitude of v = \(\sqrt {2.1^2+0.5^2} = .. \) there is no need of doing complex divisions :)
hartnn
  • hartnn
1.6*(-2.1) + 3.3*(-0.5) = -5.01
anonymous
  • anonymous
So the numerator is -5.01 and the denominator is about 2.16 and you would divide that?
hartnn
  • hartnn
thats right that will give you the magnitude of the projection vector :)
anonymous
  • anonymous
About -2.32
hartnn
  • hartnn
thats the magnitude, now you only need the direction of projection vector and since projection is along the vector 'v' its direction will be same as that of vector v !
hartnn
  • hartnn
for that, you'll need to find the unit vector in the direction of v and then mutiply the above answer to it.
anonymous
  • anonymous
Wouldn't "b" be the direction? (-2.1i -0.5j)
hartnn
  • hartnn
you need projection of vector u along vector 'v' so its direction will be along vector 'v' whats b and where it came form ?
hartnn
  • hartnn
unit vector along v = v/ |v| and we already know |v| = 2.16
hartnn
  • hartnn
so unit vector along v = (-2.1i -0.5j)/ 2.16 and your projection will be -2.32 times the above answer
anonymous
  • anonymous
(-2.1i -0.5j)/ 2.16 Would that be (-0.97i -0.23)?
hartnn
  • hartnn
what do u get after multiplying that with -2.32?
anonymous
  • anonymous
-2.32 (-0.97i -0.23) = (-2.25i -0.53j)
hartnn
  • hartnn
two negatives become positive! and you can approximate 2.25 to 2.3 and 0.53 to 0.5 :)
hartnn
  • hartnn
-2.32 * -0.97 = +2.3 -2.32 * -0.23 = +0.5
anonymous
  • anonymous
Oops! I didn't even see the double negatives. Thank you for catching that. So the answer would be B. (2.3i +0.5j)
hartnn
  • hartnn
yes, correct! good work :)
anonymous
  • anonymous
Thank you for your help. :)
hartnn
  • hartnn
most welcome ^_^

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