Vector
Is 3.00 units in length and points along the positive x axis;vector
Is 5.00 units in length and points along a direction 150° from the positive x axis.What is the direction of their sum with respect to the positive x axis?
A)62.0°
B)13.0°
C)118°
D)103°

Question

Vector 
Is 3.00 units in length and points along the positive x axis;vector 
Is 5.00 units in length and points along a direction 150° from the positive x axis.What is the direction of their sum with respect to the positive x axis?
A)62.0° 
B)13.0° 
C)118° 
D)103°

Quizplus · Accepted Answer

We can add the two vectors graphically by placing the tail of the second vector at the head of the first vector and then drawing the resultant vector from the tail of the first vector to the head of the second vector.

Alternatively, we can add the vectors using their components. The first vector has components (3,0) and the second vector has components (5cos150°,5sin150°) = (-2.55, -4.33).

The sum of the two vectors can be found by adding their corresponding components:

(3,0) + (-2.55, -4.33) = (0.45, -4.33)

The direction of the resultant vector with respect to the positive x axis can be found using trigonometry:

θ = tan⁻¹(-4.33/0.45) ≈ 118°

Therefore, the answer is C, 118°.

Vector Is 3.00 Units in Length and Points Along the Positive