Introduction To Three Dimensional Geometry

Reflexion of any point in -plane is
Reflexion of in -plane is

According to the question.

Distance of any point from -plane is

If the 4th, 10th, and 16th terms of a G.P. are , , and respectively, then:

Step 1: General formula for the nth term of a G.P.
The general formula for the nth term of a geometric progression (G.P.) is given by: where is the first term and is the common ratio of the G.P.

Step 2: Express the 4th, 10th, and 16th terms in terms of and
- The 4th term, , is given by: - The 10th term, , is given by: - The 16th term, , is given by:

Step 3: Set up a system of equations
From the above, we have the following equations:

Step 4: Solve the system of equations
To find relationships between , , and , divide Equation 2 by Equation 1: Now, divide Equation 3 by Equation 2: From Equations 4 and 5, we get: Simplifying:

Step 5: Conclusion
Therefore, the relationship between , , and is: This is the required result.

The number of diagonals that can be drawn in an octagon is:

Step 1: Formula for the number of diagonals
The formula to calculate the number of diagonals in a polygon with sides is: where is the number of sides (or vertices) of the polygon.

Step 2: Apply the formula for an octagon
An octagon has sides. Substituting this value into the formula:

Step 3: Conclusion
Therefore, the number of diagonals that can be drawn in an octagon is .