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

1. sam30317 Group Title

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

2. dumbcow Group Title

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 Group Title

4. sam30317 Group Title

.....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 Group Title

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 Group Title

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

7. sam30317 Group Title

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

8. wasiqss Group Title

dumb cow is correct ,

9. wasiqss Group Title

10. wasiqss Group Title

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

11. sam30317 Group Title

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 Group Title

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

13. wasiqss Group Title

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

14. Zara26 Group Title

thankss

15. FoolForMath Group Title

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

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

17. FoolForMath Group Title

@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 Group Title

foolformath's right

19. dumbcow Group Title

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