hello friends this video introduction to 3d matrix is brought to you by exam fear calm no more fear from exam before watching this video please make sure that you have watched part 1 to part 4 in this example we have to find the coordinates in the centroid will triangle is what is our x1 y1 z1 x2 y2 z2 and x3 y3 z3 so what we are given we are given that there is a triangle here this is x1 y1 z1 x2 y2 z2 and this is x3 y3 z3 right there suppose this point is p1 this is p2 this is P we have to find centroid to find sign point first you have to find the midpoint of this and then we have to divide at that point in to which to one ratio all right so let's suppose this point is Q and this point is our R is the centroid so first let's find the value of point Q correct so Q will be P 1 plus P 2 by 2 because it is a midpoint here so Q will nothing mean but X 1 plus X 2 by 2 comma Y 1 plus y 2 by 2 comma Z 1 plus Z 2 by this is the value of point Q correct now we have this point Q and we have this point P 3 now P 3 and Q both divides into 2 is to 1 ratio now you to find the value of r r will come out to be 2 into Q I'll say R is nothing but 2q plus P by 2 plus 1 correct that is the image to animilitia so they'll say 2 into Q always that is 2 into X 1 plus X 2 by 2 plus T 3 that is X 3 by 2 plus 1 similarly this will be 2 into y 1 plus y 2 by 2 plus y 3 by 3 comma 2 into Z 1 plus Z 2 by 2 plus Z 3 by correct this by 2 by 2 cancels bye - bye - ensign bye - bye - bye sir so what we got our is nothing but X 1 plus X 2 plus X 3 by 3 comma y 1 plus y 2 plus y 3 by 3 is 3 comma Z 1 plus Z 2 plus Z 3 by this is the value a apart so if you want to find the centroid of the triangle that is X 1 plus X 2 plus X 3 by 3 y 1 plus y 2 plus y 3 by 3 3 by 3 we have XY X 1 y 1 then 1 X 2 y 2 Z 2 X 3 by 3 3 all these are coordinates on the points of the triangle what we have done we have just found point Q there is a midpoint of P 1 and P 2 and then we are bound for the point R that is this is divided the line PQ in 2 is to 1 ratio will take for example we have to find the ratio in which the line segment joining 4 8 10 and 6 10 minus 8 is divided by why is that a plane it is something like this we have this point I suppose this P this is Q so we have point P and Q and then there is a line that is why is that plain why is that plain this divides this be queuing in let's suppose K store direction you have to find the cage to one ratio actually so if it is wise that plane we can say that X will be 0 correct because in case our Y Z plane x value 0 so let's find the x coordinate in this case so this is hole 8 10 and this is 6 10 - and let's suppose this point is o so our X that is X off point are there is nothing but K into 6 k into 6 plus 4 into 1 by k plus 1 and this dial is equal to 0 we are told correct so we get 6 k plus 4 is going to 0 or he is equal to minus 2 by 3 st. is minus 2 by 3 then we can say that this ratio is 2 by 3 and this is externally correct what we have done very simple we have got this point and we know that X in Y Z plane X equal to 0 here we have to find the coordinate of the point which trisect the line so I need P and Q where P is 4 2 minus X and Q is 10 minus 16 and 6 let's see what we are trying to say here let's draw the line first so let's suppose this is our line this is the point B and it is the point Q now we are saying it twice X that means it is three equal parts and let's suppose this is point a and this point is B me and we have to find the value of a and B where P point is given that is 4 2 minus 6 and Q point is given that is 10 minus 16 and 6 we have to find a and B now since these are all equal part this is all equal part so we can say that a divides in ratio 1 is to do correct because this is one part this is two part also we can say that B divides into each to one ratio because this part is to end this part is 1 so what do you have to do we have to just find the value of a and B we know the ratio at which this point divides P and Q so we can say that a is nothing but so this a ax is nothing but 10 into 1 plus 2 into 4 by 2 plus 1 correct and that comes out to be 10 plus in a 18 by 3 that is 6 this ax similarly a Y comes out to be 1 into minus 16 plus 2 into 2 by 2 plus 1 and that value is nothing but minus 16 plus 4 is minus 12 by 3 is minus 4 similarly easy turns out to be 1 into 6 plus 2 into minus 6 by 2 plus 1 and that value comes out to be 6 minus 12 is minus 6 by 3 is minus 2 so we know that a point is nothing but 6 minus 4 and minus 2 similarly point B if you have to find B is nothing but because this is in the 2 is to 1 ratio so this will be 2 into 10 plus 1 into 4 by 2 plus 1 this point will be 2 into minus 16 plus 1 into 12 by 2 plus 1 and this point will be 2 into 6 plus minus 1 into 6 right by 2 plus correct so this value comes out to be 4 plus 12 16 plus 20 is 20 4 by 3 that is 8 this is minus 32 plus 12 that is - strain - 32 plus 12 that is minus 20 by 3 correct this is this is the minus 6 32 plus 2 because this is wine to do that is minus 30 by 3 that is minus 10 and this is 12 minus 6 is 6 by 3 that is so v-point is nothing but 8 minus 10 and so we have to find according to the point which slicing this line so the coordinates are nothing but a and B where AR is 6 minus 4 and minus 2 and this is a and B is equal to 8 minus 10 and that is answer so what we have done we have just plotted this point P and Q and we have found a point a and B a and all these are equal so a divide this line into 1 by 2 ratio and be revised design into evolution and then we have used this formula to get the value of a and B thank you visit exam viacom to watch free education videos try free online test get the best quality study materials study from the best tutors and mentors and mushroom thanks the screen
Video Description: Examples : Part 2 - Introduction to Three Dimensional Geometry for Commerce 2023 is part of Mathematics (Maths) Class 11 preparation.
The notes and questions for Examples : Part 2 - Introduction to Three Dimensional Geometry have been prepared according to the Commerce exam syllabus.
Information about Examples : Part 2 - Introduction to Three Dimensional Geometry covers all important topics for Commerce 2023 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Examples : Part 2 - Introduction to Three Dimensional Geometry.
Introduction of Examples : Part 2 - Introduction to Three Dimensional Geometry in English is available as part of our Mathematics (Maths) Class 11 for Commerce & Examples : Part 2 - Introduction to Three Dimensional Geometry in
Hindi for Mathematics (Maths) Class 11 course. Download more important topics related with notes, lectures and mock test series for
Commerce Exam by signing up for free.
Video Lecture & Questions for Examples : Part 2 - Introduction to Three Dimensional Geometry Video Lecture | Mathematics (Maths) Class 11 - Commerce - Commerce full syllabus preparation | Free video for Commerce exam to prepare for Mathematics (Maths) Class 11.
Information about Examples : Part 2 - Introduction to Three Dimensional Geometry
Here you can find the meaning of Examples : Part 2 - Introduction to Three Dimensional Geometry defined & explained in the simplest way possible.
Besides explaining types of Examples : Part 2 - Introduction to Three Dimensional Geometry theory, EduRev gives you an ample number of questions to practice Examples : Part 2 - Introduction to Three Dimensional Geometry tests,
examples and also practice Commerce tests.