Question

for the vectors u and w with angle θ between them sketch the resultant.|u| = 18, |w| = 21, θ = 35°choose the correct sketch of the resultant below.

Explanation:

To determine the correct sketch of the resultant vector of vectors \( \mathbf{u} \) and \( \mathbf{w} \), we use the triangle law of vector addition (or parallelogram law). The triangle law states that to add two vectors, we place the tail of the second vector at the head of the first vector, and the resultant vector is drawn from the tail of the first vector to the head of the second vector.

• For vectors \( \mathbf{u} \) and \( \mathbf{w} \) with an angle \( \theta = 35^\circ \) between them, the resultant \( \mathbf{u} + \mathbf{w} \) should follow the triangle law:
• Place the tail of \( \mathbf{w} \) at the head of \( \mathbf{u} \) (or vice versa).
• The resultant vector connects the tail of the first vector to the head of the second vector.

Looking at the options:

• Option B shows \( \mathbf{u} \) and \( \mathbf{w} \) arranged such that the tail of \( \mathbf{w} \) (or \( \mathbf{u} \)) is at the head of the other, and the resultant (red arrow) connects the tail of the first to the head of the second—consistent with the triangle law.
• Options A and C do not align with the triangle law of vector addition (e.g., A shows a different configuration, C shows a symmetric/opposite arrangement inconsistent with the given angle).

Answer:

B. (The sketch in Option B, where the resultant vector is drawn from the tail of one vector to the head of the other, following the triangle law of vector addition.)