Question

given the vectors a and b, sketch the vector a + b. choose the correct sketch of a + b below. o a. o b. o c. o d.

Explanation:

Step1: Recall Vector Addition (Triangle Law)

The triangle law of vector addition states that to add two vectors \(\vec{a}\) and \(\vec{b}\), we place the tail of \(\vec{b}\) at the head of \(\vec{a}\). The resultant vector \(\vec{a}+\vec{b}\) is then drawn from the tail of \(\vec{a}\) to the head of \(\vec{b}\).

Step2: Analyze Each Option

• Option A: The tail of \(\vec{b}\) is not at the head of \(\vec{a}\), so this does not follow the triangle law.
• Option B: Here, the tail of \(\vec{b}\) is at the head of \(\vec{a}\), and the resultant \(\vec{a}+\vec{b}\) is drawn from the tail of \(\vec{a}\) to the head of \(\vec{b}\), which follows the triangle law of vector addition.
• Option C: The direction of \(\vec{b}\) or the placement does not align with the triangle law for \(\vec{a}+\vec{b}\).
• Option D: The configuration does not follow the triangle law for adding \(\vec{a}\) and \(\vec{b}\).

Answer:

B. (The option with the correct vector addition sketch as per the triangle law)