Vector = 1.00
+ -2.00
And vector
= 3.00
+ 4.00
. What are the magnitude and direction of vector
=
+
?

Question

Vector  = 1.00 
+ -2.00 
And vector 
= 3.00 
+ 4.00 
. What are the magnitude and direction of vector 
= 
+ 
?

Quizplus · Accepted Answer

To find the magnitude and direction of the vector, we need to add up the x and y components of the given vectors:

11eab6cc_1d8f_104b_a957_f1e50fda911b_TB4469_11 = (1.00 + 3.00) 11eab6cc_1d8e_9b15_a957_0337a7c4dbdc_TB4469_11 + (-2.00 + 4.00) 11eab6cc_1d8e_e938_a957_27399a62bd41_TB4469_11

= 4.00 11eab6cc_1d8e_9b15_a957_0337a7c4dbdc_TB4469_11 + 2.00 11eab6cc_1d8e_e938_a957_27399a62bd41_TB4469_11

The x-component of this vector is:

4.00 cos(33.7°) + 2.00 cos(63.4°) = 2.926

The y-component of the vector is:

4.00 sin(33.7°) + 2.00 sin(63.4°) = 3.842

Using the Pythagorean theorem, the magnitude of the vector is:

sqrt[(2.926)^2 + (3.842)^2] = 4.47

The angle between the vector and the positive x-axis is:

arctan[(3.842)/(2.926)] = 53.4°

Since the vector is in the second quadrant, we need to add 180° to this angle to get the final answer, which is:

180° + 53.4° = 233.4°

Finally, we subtract this angle from 360° to get the angle counterclockwise from the positive x-axis:

360° - 233.4° = 126.6°

So the answer is D) 4.47 in a direction 26.6° counterclockwise from the positive x-axis.