Question

Given $\vec{a}$ and $\vec{b}$ are two vectors, $\vec{a}\cdot\vec{b}=?$}

• A. $ab\sin\theta$
• B. $ab\cos\theta$
• C. $ab\sin\theta$
• D. $ab\cos\theta$

Hint:

Dot product always involves cosine of angle between vectors.

Answer 1

The Correct Option is B

Concept:
Dot product of two vectors depends on magnitudes and angle between them.
Step 1:
The scalar product is given by: \[ \vec{a}\cdot\vec{b}=ab\cos\theta \]
Step 2:
Where:
• \(a\) and \(b\) are magnitudes
• \(\theta\) is angle between vectors
Step 3:
Dot product gives scalar quantity.
Step 4:
Hence: \[ \boxed{\vec{a}\cdot\vec{b}=ab\cos\theta} \] \[ \boxed{\text{Correct Option = (2)}} \]