Question

how to add vectors (1,1,1) and (0,2,1)??

Answer 1

(1+0) + (1+2) + (1+1)

Answer 2

dont you have to use parellalogram method for addition?

Answer 3

Two vectors can be combined by adding their corresponding components together.
i.e. (vx, vy, vz) + (wx, wy, wz) is (vx+wx, vy+wy, vz+wz ).

(1,1,1) + (0,2,1) = (1+0) + (1+2) + (1+1)

Answer 4

thank you :) :D

Answer 5

you're welcome :)

Answer 6

@zaisav , should we change the notation from

(1,1,1) + (0,2,1) = (1+0) + (1+2) + (1+1)

to

(1,1,1) + (0,2,1) = ((1+0) , (1+2) , (1+1))

? After all, the vector sum is a vector, and so it must have components.

If you want to do something similar to that, you can use unit vector notation. In that, each part ( (1+0) , (1+2) , and (1+1) ) would be scalars, and they would multiply a unit vector. The unit vector gives the scalar direction, and the scalar gives the unit vector magnitude that might be different from \(1\). If you have questions on unit vectors (for ANYONE who hasn't learned about them), please ask!

Common unit vectors use the letters i, j, and k. Many math textbooks use bold or an arrow to indicate a vector, like \(\boldsymbol i = \overrightarrow i\). I hink I heard that physicist often use a "hat," like \(\hat i\). So, if the unit vectors are \(\hat i\), \(\hat j\), and \(\hat k\), we'd have

\((1,1,1) + (0,2,1) = (1+0)\hat i + (1+2)\hat j + (1+1)\hat k\)

which looks very similar to your response, zaisav!

Answer 7

@theEric you're absolutely right about that :)