Vector is 3.0 units in length and points along the positive x-axis;vector is 4.0 units in length and points along a direction 150 $\degree$from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?
A)77 $\degree$
B)13 $\degree$
C)86 $\degree$
D)103 $\degree$

Question

Vector  is 3.0 units in length and points along the positive x-axis;vector  is 4.0 units in length and points along a direction 150 $\degree$from the positive x-axis.What is the direction of the resultant with respect to the positive x-axis?
A)77 $\degree$ 
B)13 $\degree$ 
C)86 $\degree$ 
D)103 $\degree$

Quizplus · Accepted Answer

To find the direction of the resultant, we need to first calculate the angle that vector 11eaa64f_8f76_3f9a_a696_bdf9d35c511c_TB5258_11 makes with the positive x-axis:

angle = 150 degrees - 180 degrees = -30 degrees

Note that we subtract 180 degrees from 150 degrees because the angle is measured clockwise from the positive x-axis.

Next, we can use the cosine law to find the angle between the resultant and the positive x-axis:

cos(theta) = (3^2 + 4^2 - 2(3)(4)cos(-30 degrees)) / (2(3)(4))

cos(theta) = 0.9167

theta = cos^-1(0.9167) = 22.6 degrees

Finally, because the angle between vector 11eaa64f_8f76_3f99_a696_038fe9b42aa9_TB5258_11 and the positive x-axis is 0 degrees, the direction of the resultant with respect to the positive x-axis is:

22.6 degrees - 0 degrees = 22.6 degrees

Therefore, the answer is D) 103 degrees.

Vector Is 3 °\degree° From the Positive X-Axis °\degree° B)13 °\degree° C)86 °\degree°

Vector Is 3 $\degree$ From the Positive X-Axis $\degree$ B)13 $\degree$ C)86 $\degree$