The correct answer is B because:

Method 1

Using either the triangle or parallelogram method it’s possible to determine the direction of the resulting vector

In both methods, you must slide the vectors, parallel to their current direction, so that they are arranged tip to tail
The resultant vector is the one now joining from tail to tip on the other side
The 120° angle will be on the outside of the triangle or parallelogram

The resultant vector is the same length as the 10 N vectors, as the diagram is drawn to scale

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Method 2

Consider the cosine rule to find the length of the resultant side:
- $a^{2} = b^{2} + c^{2} - 2 b c \cos (A)$
- Label the angles and sides of the triangle

file-000-13

Substitute in the known sides and angle
- $a^{2} = 10^{2} + 10^{2} - 2 \times 10 \times 10 \times \cos (60)$
Calculate the length of the resultant side a:
- a = 10 N
Consider the sine rule to find the angle of the resultant side to the horizontal:
- $\frac{a}{\sin (A)} = \frac{c}{\sin (C)}$
Substitute in the known sides and angle:
- $\frac{10}{\sin (60)} = \frac{10}{\sin (C)}$
Rearrange the equation and calculate the angle of the resultant side to the horizontal:
- - $10 \times \sin (C) = 10 \times \sin (60)$
  - $\sin (C) = \sin (60)$
  - So, C = 60°

Scalars & Vectors (CIE A Level Physics)

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