Question

find the components of the vector 3i+2j+8k in the direction of the vector 2i+2j+2k

Answer 1

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

Answer 2

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

Answer 3

r u sure about the answer

Answer 4

.....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

Answer 5

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?

Answer 6

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

Answer 7

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

Answer 8

dumb cow is correct ,

Answer 9

wait, ik the right answer.

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

thankss

Answer 15

\(<3,2,8> . <2,2,2> = 6 + 4+16 = 26\)

\[|<2,2,2>|= \sqrt{12} \]

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, \(\frac {26}{12} <2,2,2> = \frac {13}6<2,2,2> \)

Answer 16

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

Answer 17

@dumbcow: I am not sure from where you came up with that definition, can you please explain?

http://en.wikipedia.org/wiki/Vector_projection

Answer 18

foolformath's right

Answer 19

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