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The coordinates of a point are (1,-3,3),...

The coordinates of a point are (1,-3,3), the point lies in

A

(a)II octant

B

(b)VIII octant

C

(c)I octant

D

(d)IV octant

Text Solution

AI Generated Solution

The correct Answer is:
To determine in which octant the point with coordinates (1, -3, 3) lies, we need to analyze the signs of the coordinates (x, y, z). ### Step-by-Step Solution: 1. **Identify the coordinates**: The given point is (1, -3, 3), where: - x = 1 - y = -3 - z = 3 2. **Determine the sign of each coordinate**: - The x-coordinate (1) is positive. - The y-coordinate (-3) is negative. - The z-coordinate (3) is positive. 3. **Recall the octants in 3D space**: The three-dimensional space is divided into eight octants based on the signs of the coordinates: - Octant I: (+, +, +) - Octant II: (-, +, +) - Octant III: (-, -, +) - Octant IV: (+, -, +) - Octant V: (+, +, -) - Octant VI: (-, +, -) - Octant VII: (-, -, -) - Octant VIII: (+, -, -) 4. **Match the signs to the octants**: - For our point (1, -3, 3): - x is positive (+) - y is negative (-) - z is positive (+) - This corresponds to Octant IV, where the signs of the coordinates are (+, -, +). 5. **Conclusion**: The point (1, -3, 3) lies in the fourth octant. ### Final Answer: The point (1, -3, 3) lies in the fourth octant.
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