If vector and vector ,where and are the units vectors along the x and the y directions respectively.If ,calculate the angle vector makes with respect to the +x axes.
A)-84º
B)-96º
C)84º
D)96º
E)-6º

Question

If vector  and vector  ,where  and  are the units vectors along the x and the y directions respectively.If  ,calculate the angle vector  makes with respect to the +x axes.
A)-84º 
B)-96º 
C)84º 
D)96º 
E)-6º

Quizplus · Accepted Answer

First, we need to find the vector between the two given vectors:

11ea821f_c6d8_42f3_bbd8_437693a84fb8_TB1516_11_TB1516_11_TB1516_11 - 11ea821f_c6d8_42f2_bbd8_e7d609372ca4_TB1516_11_TB1516_11_TB1516_11
= 11ea821f_c6d8_6a06_bbd8_7b266cb346e9_TB1516_11_TB1516_11_TB1516_11

Now, we can calculate the angle that this vector makes with the +x axis using the arctan function and the x and y components of the vector:

angle = arctan(y-component / x-component)
angle = arctan(11ea821f_c6d8_6a05_bbd8_b53df5897194_TB1516_11_TB1516_11_TB1516_11 / 11ea821f_c6d8_42f4_bbd8_15f3f311dbe2_TB1516_11_TB1516_11_TB1516_11)
angle = arctan(1)
angle ≈ 45º

Since the vector is in the second quadrant, we need to add 180º to the angle:

angle = 45º + 180º = 225º

However, we need to express the answer in terms of a negative angle between -180º and 180º. Therefore, we subtract 360º from the angle:

angle = 225º - 360º = -135º

Finally, we add 180º to obtain the angle with respect to the +x axis:

angle = -135º + 180º = 45º

Therefore, the angle that vector 11ea821f_c6d8_6a07_bbd8_bb5c4ec91fc1_TB1516_11_TB1516_11_TB1516_11 makes with respect to the +x axis is 45º, which corresponds to choice D.

If Vector and Vector ,Where and