Question

for the vectors u and w with angle θ between them sketch the resultant

u

= 12,

w

= 29, θ = 37°

choose the correct sketch of the resultant below
○ a.
○ b.
○ c.

Explanation:

Step1: Recall the parallelogram law of vector addition

When adding two vectors \(u\) and \(w\), we place them tail - to - tail. Then we complete the parallelogram. The resultant vector (the sum \(u + w\)) is the diagonal of the parallelogram starting from the common tail of \(u\) and \(w\).

Step2: Analyze each option

• Option A: It correctly represents the parallelogram law of vector addition. The vectors \(u\) and \(w\) are tail - to - tail, and the resultant (the red vector) is the diagonal of the parallelogram formed by \(u\) and \(w\).
• Option B: This does not follow the parallelogram law. In the parallelogram law, vectors are tail - to - tail, but here the resultant is drawn in a way that does not complete the parallelogram structure.
• Option C: The orientation of the vectors and the resultant is incorrect. The common starting point of the vectors for the parallelogram law is not maintained as per the standard vector - addition (parallelogram) rule.

Answer:

A.