Question

The vector equation of the XY-plane is

• A. \vecr \cdot \hatk = 0
• B. \vecr \cdot \hatj = 0
• C. \vecr \cdot \hati = 0
• D.

Hint:

For any plane, the vector equation can often be expressed as the dot product of the position vector with a normal vector to the plane, which equals zero.

Answer 1

The Correct Option is A

Step 1: Equation of the XY-plane.
The equation of the XY-plane in vector form can be written as: \[ \vecr \cdot \hatk = 0 \] This is because the position vector \vecr lies in the XY-plane, and any vector in this plane is perpendicular to the unit vector \hatk in the Z-direction. Thus, their dot product is zero. Step 2: Conclusion.
Therefore, the correct vector equation of the XY-plane is \vecr \cdot \hatk = 0 . Final Answer: \vecr \cdot \hatk = 0 .