Earlier we have discussed and practiced o probability worksheets and Today we are going to learn about Planar cross sections; perpendicular lines, planes in XI Grade of gujarat state education board.
Here is about planar cross sections and math questions related to it:
planar cross-sections
We can define planar –cross sections as the figure formed when the plane intersects a solid figure.the result of intersection thus comes out to be a line,line segment or a plane figure such as a circle or a polygon.
There are however certain conditions related to planar cross sections
Like if plane is parallel to the base of the solid ,the plain figure thus formed will be similar or congruent to the base of solid.(want to Learn more about Cross Sections ,click here),
Now we further move to the next topic of Grade XI called as the perpendicular lines
What are perpendicular lines?
·A perpendicular lines ,is a line that intersects another line or a plane such that the angle formed by their intersection is exactly 90 degrees . in other words, a right angle. In geometry, such lines are represented by a symbol (⊥) that resembles an upside down T --- that letter being an example of two perpendicular lines joining together. Perpendicular lines and parallel lines share a relationship; if two lines are both perpendicular to a third line, they are parallel to each other . if we extended them indefinitely, the lines will never touch.
Now we learn about the planes related to Grade XI
In mathematics a plane is a flat two dimensional suface .A plane is the two dimensional figure of a point,a line and a space.planes can arise as subspaces of some higher dimensional spacesas with walls of rooms.
In a three-dimensional space, another important way of defining a plane is by specifying a point and a normal vector to the plane.
Let r0 be the position vector of some known point P0 in the plane, and let n be a nonzero vector normal to the plane. The idea is that a point P with position vector r is in the plane if and only if the vector drawn from P0 to P is perpendicular to n. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be expressed as the set of all points r such that
n.. (r-r0)= 0
now we have discussed in detail about the three topics related to Grade XI ie.planar cross section,perpendicular lines an planes.
Thus to sum up we can say that all the three topics are related to each other and are the important part of Grade XI mathematics and if you want to know about Correlation coefficient and about grade 10th topic Fundamental theorem of algebra then refer Internet.
Here is about planar cross sections and math questions related to it:
planar cross-sections
We can define planar –cross sections as the figure formed when the plane intersects a solid figure.the result of intersection thus comes out to be a line,line segment or a plane figure such as a circle or a polygon.
There are however certain conditions related to planar cross sections
Like if plane is parallel to the base of the solid ,the plain figure thus formed will be similar or congruent to the base of solid.(want to Learn more about Cross Sections ,click here),
Now we further move to the next topic of Grade XI called as the perpendicular lines
What are perpendicular lines?
·A perpendicular lines ,is a line that intersects another line or a plane such that the angle formed by their intersection is exactly 90 degrees . in other words, a right angle. In geometry, such lines are represented by a symbol (⊥) that resembles an upside down T --- that letter being an example of two perpendicular lines joining together. Perpendicular lines and parallel lines share a relationship; if two lines are both perpendicular to a third line, they are parallel to each other . if we extended them indefinitely, the lines will never touch.
Perpendicular Lines Equation
The equation for perpendicular line i.e the linear equation is "linear equation" is "y = mx + c" .Perpendicular Lines use in the Real World
·Most perpendicular lines in the real world are man-made; the capital letter "H," for example, consists of two parallel lines with a line connecting them in perpendicular fashion. Like many examples that are perfect mathematically, perpendicularity in the real world is complicated by the lack of any truly flat planes. Eg A skyscraper.Now we learn about the planes related to Grade XI
In mathematics a plane is a flat two dimensional suface .A plane is the two dimensional figure of a point,a line and a space.planes can arise as subspaces of some higher dimensional spacesas with walls of rooms.
In a three-dimensional space, another important way of defining a plane is by specifying a point and a normal vector to the plane.
Let r0 be the position vector of some known point P0 in the plane, and let n be a nonzero vector normal to the plane. The idea is that a point P with position vector r is in the plane if and only if the vector drawn from P0 to P is perpendicular to n. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be expressed as the set of all points r such that
n.. (r-r0)= 0
now we have discussed in detail about the three topics related to Grade XI ie.planar cross section,perpendicular lines an planes.
Thus to sum up we can say that all the three topics are related to each other and are the important part of Grade XI mathematics and if you want to know about Correlation coefficient and about grade 10th topic Fundamental theorem of algebra then refer Internet.
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