Find the magnitude of the vector and the angle , , that the vector makes with the positive x -axis.
A)
B)
D)

Question

Find the magnitude of the vector and the angle  ,   , that the vector makes with the positive x -axis. ​  ​
A)​ 
B)​ 
D)​

Quizplus · Accepted Answer

To find the magnitude of the vector, we use the Pythagorean theorem:

|v| = sqrt((11ebf5ef_bbd4_3f74_95d1_374818722344_TBX9354_11)^2 + (11ebf5ef_bbd4_3f75_95d1_a9ce47ffc271_TBX9354_11)^2 + (11ebf5ef_bbd4_6686_95d1_4f3fdaa1cf9f_TBX9354_11)^2)
    = sqrt(3)

To find the angle that the vector makes with the positive x-axis, we use the dot product:

v . i = |v| |i| cos(theta)
where i = (1,0,0) is the unit vector along the positive x-axis.

v . i = 11ebf5ef_bbd4_3f74_95d1_374818722344_TBX9354_11
theta = arccos(v . i / |v| |i|)
      = 45 degrees

Therefore, the best choice is C.

Find the Magnitude of the Vector and the Angle