## Zara26 3 years ago find the components of the vector 3i+2j+8k in the direction of the vector 2i+2j+2k

1. sam30317

3i+2j+8k +2i+2j+2k ______________ 5i +4j +10k Check if its right. Been a looong time since ive done this.

2. 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

3. Zara26

4. sam30317

.....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

5. 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?

6. Zara26

am not sure...am still trying to solve it

7. sam30317

R u doing college physics?? Did u read anything about "dot product"??

8. wasiqss

dumb cow is correct ,

9. wasiqss

10. wasiqss

we take the dot product of first vector with unit vector of second

11. sam30317

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

12. sam30317

Yeaaah!! I dont remember how to get angle..if its needed

13. wasiqss

zara my answer is the right one, cause i did this question last day

14. Zara26

thankss

15. FoolForMath

$$<3,2,8> . <2,2,2> = 6 + 4+16 = 26$$ $|<2,2,2>|= \sqrt{12}$ 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, $$\frac {26}{12} <2,2,2> = \frac {13}6<2,2,2>$$

16. FoolForMath

I have assumed that you meant vector component and not the scalar one.

17. FoolForMath

@dumbcow: I am not sure from where you came up with that definition, can you please explain? http://en.wikipedia.org/wiki/Vector_projection

18. anonymoustwo44

foolformath's right

19. dumbcow

@foolFormath, oops did not recognize this as vector projection...for some reason i thought the magnitude of 1st vector should remain the same