anonymous
  • anonymous
find the components of the vector 3i+2j+8k in the direction of the vector 2i+2j+2k
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
3i+2j+8k +2i+2j+2k ______________ 5i +4j +10k Check if its right. Been a looong time since ive done this.
dumbcow
  • dumbcow
im guessing find magnitude of 1st vector --> sqrt(3^2 + 2^2+8^2) = sqrt(77) and then find components of directional vector with same magnitude unit vector of 2nd vector = 1/sqrt3 , 1/sqrt3 , 1/sqrt3 multiply by magnitude --> sqrt(77/3) i + sqrt(77/3) j + sqrt(77/3) k
anonymous
  • anonymous
r u sure about the answer

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anonymous
  • anonymous
.....NO!!! Im not confident thats right. I suggest asking this question in the physics study group. And look at t his site: http://www.ehow.com/how_8396057_determine-resultant-vector.html
dumbcow
  • dumbcow
im pretty sure i did it right as long as i understood the question correctly. you taking 1st vector and placing it so its going same direction as 2nd vector but has same magnitude...correct?
anonymous
  • anonymous
am not sure...am still trying to solve it
anonymous
  • anonymous
R u doing college physics?? Did u read anything about "dot product"??
wasiqss
  • wasiqss
dumb cow is correct ,
wasiqss
  • wasiqss
wait, ik the right answer.
wasiqss
  • wasiqss
we take the dot product of first vector with unit vector of second
anonymous
  • anonymous
Instead of adding, do what I showed you in the SAME set up, except u multiply straight down: (3*2)+(2*2)+(8*2) = 26
anonymous
  • anonymous
Yeaaah!! I dont remember how to get angle..if its needed
wasiqss
  • wasiqss
zara my answer is the right one, cause i did this question last day
anonymous
  • anonymous
thankss
anonymous
  • anonymous
\(<3,2,8> . <2,2,2> = 6 + 4+16 = 26\) \[|<2,2,2>|= \sqrt{12} \] Vector component of \(\vec{a} \)in the direction of \(\vec{b}\) is given by \( \frac {\mathbf{a} \cdot \mathbf{b}} {|\mathbf{b}| } \frac {\mathbf{b}} {|\mathbf{b}|} \) Hence, \(\frac {26}{12} <2,2,2> = \frac {13}6<2,2,2> \)
anonymous
  • anonymous
I have assumed that you meant vector component and not the scalar one.
anonymous
  • anonymous
@dumbcow: I am not sure from where you came up with that definition, can you please explain? http://en.wikipedia.org/wiki/Vector_projection
anonymous
  • anonymous
foolformath's right
dumbcow
  • dumbcow
@foolFormath, oops did not recognize this as vector projection...for some reason i thought the magnitude of 1st vector should remain the same

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