Respuesta :
Answer:
The answer is "26.3 m".
Explanation:
The positive value from the x-axis is to the direction east side
The negative value from the x-axis is to the direction west side
The positive value from the y-axis is to the direction upwards side
The negative value from the y-axis is to the direction down words side
The positive value from the z-axis is to the direction southside
The negative value from the z-axis is to the direction north side
If the value is i, j, and k are the unit of the given vectors, which can be defined as follows:
[tex]\hat i, \hat -i, \hat j, \hat -j, \hat k, \hat -k[/tex]
The displacements values:
[tex]\underset{d_1}{\rightarrow} = -14 \ \hat i\\\\\underset{d_2}{\rightarrow} = 22\ \hat j\\\\\underset{d_3}{\rightarrow} = -12 \ \hat k\\\\\underset{d_4}{\rightarrow} = 6 \ \hat i\\\\[/tex]
calculating the final displacement that is [tex]\underset{d_5}{\rightarrow}[/tex]:
[tex]\Rightarrow \underset{d_1}{\rightarrow}+\underset{d_2}{\rightarrow}+\underset{d_3}{\rightarrow}+\underset{d_4}{\rightarrow}+\underset{d_5}{\rightarrow} =0\\\\\Rightarrow \underset{d_5}{\rightarrow} \ \ = -(\underset{d_1}{\rightarrow}+\underset{d_2}{\rightarrow}+\underset{d_3}{\rightarrow}+\underset{d_4}{\rightarrow})[/tex]
[tex]=- (-14 \hat i+ 22 \hat j -12 \hat k+ 6 \hat i)\\\\=- (-8 \hat i+ 22 \hat j -12 \hat k)\\\\=8 \hat i- 22 \hat j +12 \hat k\\[/tex]
[tex]|\underset{d_5}{\rightarrow}|=\sqrt{8^2 +(- 22)^2 +(12)^2 }\\\\[/tex]
[tex]= \sqrt{64 + 484 +144 }\\\\= \sqrt{208 + 484}\\\\= \sqrt{692}\\\\= 26.3 \ m[/tex]
