Question

\( \vec{A} \) and \( \vec{B} \) are two non-zero vectors inclined at an angle \( \theta \). \( \hat{a} \) and \( \hat{b} \) are unit vectors along \( \vec{A} \) and \( \vec{B} \) respectively. The component of \( \vec{A} \) in the direction of \( \vec{B} \) is

• A. \( \dfrac{\vec{A}\cdot\vec{B}}{B} \)
• B. \( \dfrac{\vec{A}\times\vec{B}}{A} \)
• C. \( \hat{a}\cdot\vec{B} \)
• D. \( \vec{A}\cdot\hat{b} \)

Hint:

Vector component along a direction is always found using dot product with the unit vector of that direction.

Answer 1

The Correct Option is D

Step 1: Definition of component of a vector.
The component of vector \( \vec{A} \) along direction of \( \vec{B} \) is given by the dot product of \( \vec{A} \) with unit vector along \( \vec{B} \).

Step 2: Write mathematical expression.
\[ \text{Component of } \vec{A} \text{ along } \vec{B} = \vec{A}\cdot\hat{b} \]

Step 3: Final conclusion.
Thus, the correct expression is \( \vec{A}\cdot\hat{b} \).