Vectors , , , and have the following components: The magnitude of the resultant is
A) - 4.6 units.
B) 5.4 units.
C) 29 units.
D) 3.5 units.
E) 7.3 units.

Question

Vectors  ,  ,  , and  have the following components:  The magnitude of the resultant is
A) - 4.6 units. 
B) 5.4 units. 
C) 29 units. 
D) 3.5 units. 
E) 7.3 units.

Quizplus · Accepted Answer

To find the resultant vector, we need to add up the components of all four vectors.
The x-component of the resultant vector is:
11eb1367_5169_80fc_8021_f52f21cb29cb_TB7291_11 + 11eb1367_5169_80fd_8021_e56dc18faec7_TB7291_11 + 11eb1367_5169_80fe_8021_63826d6ccb7e_TB7291_11 + 11eb1367_5169_80ff_8021_f38e4aa12188_TB7291_11 = 11eb1367_5169_8100_8021_71f1bf2fe1a5_TB7291_00
The y-component of the resultant vector is:
11eb1367_5169_80fc_8021_f52f21cb29cb_TB7291_11 + 11eb1367_5169_80fd_8021_e56dc18faec7_TB7291_11 + 11eb1367_5169_80fe_8021_63826d6ccb7e_TB7291_11 - 11eb1367_5169_80ff_8021_f38e4aa12188_TB7291_11 = 11eb1367_5169_8101_8021_df3c80305f62_TB7291_11
Now we can use the Pythagorean theorem to find the magnitude of the resultant vector:
|resultant| = sqrt((x-component)^2 + (y-component)^2) = sqrt((11eb1367_5169_8100_8021_71f1bf2fe1a5_TB7291_00)^2 + (11eb1367_5169_8101_8021_df3c80305f62_TB7291_11)^2) = 5.4 units.

Vectors , , , and Have