Question

Distance between \(A(1,2,3)\) and \(B(4,6,3)\):

• A. \(4\)
• B. \(5\)
• C. \(6\)
• D. \(7\)

Hint:

Distance formula in 3D: \[ d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \] It is the extension of Pythagoras theorem to space geometry.

Answer 1

The Correct Option is B

Concept: Distance between two points in 3D geometry: \[ d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2} \]

Step 1: Substituting coordinates. Points are: \[ A(1,2,3) \] and \[ B(4,6,3) \] Thus: \[ d = \sqrt{(4-1)^2+(6-2)^2+(3-3)^2} \]

Step 2: Simplifying. \[ = \sqrt{3^2+4^2+0^2} \] \[ = \sqrt{9+16} \] \[ = \sqrt{25} \] \[ =5 \] Final Answer: \[ \boxed{(B)\ 5} \]