Question

Find the dot product of the unit vectors: \[ \hat{j} \cdot \hat{j} \]

• A. 0
• B. 1
• C. -1
• D. \( \hat{k} \)

Hint:

The dot product of any unit vector with itself is always 1, since the angle between the two vectors is 0 degrees.

Answer 1

The Correct Option is B

The dot product of two unit vectors \( \hat{u} \) and \( \hat{v} \) is defined as: \[ \hat{u} \cdot \hat{v} = |\hat{u}| |\hat{v}| \cos \theta \] where \( \theta \) is the angle between the two vectors, and \( |\hat{u}| = |\hat{v}| = 1 \) for unit vectors. For \( \hat{j} \cdot \hat{j} \), the angle \( \theta \) is 0 degrees (since they are the same vector), and \( \cos(0^\circ) = 1 \). Therefore: \[ \hat{j} \cdot \hat{j} = 1 \times 1 \times 1 = 1 \] Thus, the correct answer is: \[ \boxed{1} \]