Let = (2 m) + (6 m)

Question

Let  = (2 m)  + (6 m)  - (3 m)  and  = (4 m)  + (2 m)  + (1 m)  .The vector sum  is:
A)(6 m) + (8 m) - (2 m) 
B)(−2 m) + (4 m) - (4 m) 
C)(2 m) − (4 m) + (4 m) 
D)(8 m) + (12 m) - (3 m) 
E)none of these

Quizplus · Accepted Answer

We can add the corresponding components of the vectors to find the components of the resultant vector. 
For the x-component, we have: 
2 + 6 - 3 = 5 
4 + 2 + 0 = 6 
Therefore, the x-component of the resultant vector is 5+6=11m. 
For the y-component, we have: 
0 + 0 - 0 = 0 
0 + 0 + 1 =1 
Therefore, the y-component of the resultant vector is 0+1=1m.
For the z-component, we have: 
0 + 0 - 0 = 0 
0 + 0 - 0 =0  
Therefore, the z-component of the resultant vector is 0.
So the resultant vector is (11 m) 11eab079_969d_8b5c_a51f_75a9a4e241df_TB6585_11 + (1 m) 11eab079_969d_b26d_a51f_4b511b6f948f_TB6585_11 - (0 m) 11eab079_969d_b26e_a51f_cd9dd7fd2e67_TB6585_11. Which matches with choice (A).