Q. 11 - Calculus

Question

What point is symmetric about the origin to the point \((5, −6, 7)\)?

Step-by-Step Solution

Answer

The symmetric point of \((5, -6, 7)\) about the origin is \((-5, 6, -7)\)

Step 1. Given Information

The given point is \((5, -6, 7)\).

Here, \(x\) and \(z\) are positive and the \(y\) coordinate is negative. Thus, the above point lies in the third octant.

Step 2. Finding the symmetric point

As the given point lies in the third octant, its symmetric point will lie in the sixth octant where both the x and z coordinates are negative and the y coordinate is positive.

Therefore, the symmetric point of \((5,-6,7)\) about the origin \((0,0)\)  is \((-5,6,-7)\).