NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry
FAQs on NCERT Solutions for Class 11 Maths Chapter 12: Introduction to Three Dimensional Geometry - Exercise 12.2
1. How can you determine an equation for a group of points?
How to determine a line's equation from two points:
Using the slope formula, determine the slope.
$\text{slope}=m=\dfrac{\text{rise}}{\text{run}}=\dfrac{y_2-y_1}{x_2-x_1}$
To find the y-intercept, use the slope and one of the points (b).
The x and y of your equation y = mx+b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable left is b in that case. To solve for b, use the same methods you would solve for a variable.
2. What is a section, and what is the formula for a section when a point internally divides a line connecting two points?
The coordinates of a point that divides a line segment externally or internally in some ratio can be found using the section formula. The midpoint of a line segment can be determined using this formula as well. For instance, if point P internally divides a line segment AB, then the section formula for internal division applies.
The location coordinates of a point P that internally divides the line connecting two points A(x1,y1,z1) and B(x2,y2,z2) in the m:n ratio are:
$\lgroup\dfrac{m{x}_{2}+n{x}_{1}}{m+n},\dfrac{m{y}_{2}+n{y}_{1}}{m+n},\dfrac{m{z}_{2}+n{z}_{1}}{m+n}\rgroup$
3. How to find unknown coordinates under various circumstances?
Consider unknown coordinates to be X, Y, and Z, and then substitute them for the given conditions—for example, that the given points are in an equilateral triangle or that they are equally spaced apart from one another—to find the unknown. When different conditions involving the distance formula are given, form a system of equations or a single equation using the conditions that are given, then solve this so-formed equation to find the unknown questions.
4. How can a line segment's trisection point be located?
The formula where a line is internally divided into three segments in a ratio of 1:2 or 2:1. To solve any problem, use the section formula.
Where m and n are the two numbers that make up the m:n ratio.
Use the section formula twice for the trisection formula.
First, use the m:n = 1:2 ratio to solve the line segment's points.
Step 2: Apply the m:n = 2:1 ratio to the line segment's points.
5. How can a point's locus be determined?
The locus that lies exactly midway between the two points, let's say A and B, is regarded as a perpendicular bisector of the line segment that connects the two points.
This theorem aids in determining the region that is made up of all points that are situated equally from points A and B. The perpendicular bisector of the line segment AB should be the region that is created.
Only for curved shapes is the locus defined. These forms can be regular or asymmetrical.