If
= [10 m,30°] and
= [25 m,130°],what is the direction of the sum of these two vectors?
A)17°
B)73°
C)107°
D)163°
E)100°

Question

If 
= [10 m,30°] and 
= [25 m,130°],what is the direction of the sum of these two vectors?
A)17° 
B)73° 
C)107° 
D)163° 
E)100°

Quizplus · Accepted Answer

To find the direction of the sum of vectors, we need to add the two vectors and then find the angle it makes with the positive x-axis.

Using the vector addition formula: 
[10cos(30) + 25cos(130), 10sin(30) + 25sin(130)] 
= [-8.66, 22.53]

The angle this vector makes with the positive x-axis is: 
θ = tan⁻¹(22.53/-8.66) 
θ = 107°

Therefore, the direction of the sum of these two vectors is 107°.

If = [10 M,30°] and