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samacheer kalvi class 11 maths solutions எல்லாம் ஒரே இடத்தில் இங்கு நீங்கள் பெற்றுக்கொள்ளலாம். students க்கு எந்தமாதிரி சொல்லிக்கொடுத்தால் புரியும் என்று நங்கள் ஆராய்ச்சி செய்து ஒரு புது முறையில் உங்களுக்காக வழங்குகின்றோம்.
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Here you can find solution to 80 Exercise Problems in 11th maths for Tamilnadu Samacheer Syllabus
நீங்கள் Vector Algebra ஐ எளிதாக புரிந்துகொள்ளும் வகையில் இந்த video வை நங்கள் தருகின்றோம். இதே மாதிரி video lessons உங்களுக்காக நாங்கள் தயாரித்து வைத்துளோம். நீங்கள் register செய்து தள்ளுபடியில் நீங்கள் video lessons ஐ பெறலாம்
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If we assume that you have to land a flight when the navigation system is not working. The only way to handle this is to know the vector algebra. If you are master in the subject you can easily solve the landing problem by scribbling in a piece of paper. But in real world with modern equipments these calculations are done by the computer itself. Hence we are not that aware of the application of the vector algebra which is calculated behind the scene in the equipments.
If a ball is thrown from top a high rise building, then the force that acts on the ball would be influenced by gravitational force and the wind resistance. Similarly the force that acts on a plan is the forward velocity of the plane and the resistance of the air that acts at a particular angle opposite to the flight direction. So when we look at two forces that act on an object then we need to find out the sum of effect of both the forces. The sum will then depend on whether the force acting in the same direction or different direction.
Vector finds its major use across all the flying objects like aeroplane, helicopter, rocket…etc. Also it is used in the position of the satellite and GPS systems. For the missiles and the diffensive radars the application of vector algebra is very crucial.
Vector concept is built and made popular by two famous mathematicians Grassmann from Germany and Hamilton from Irish.
At the same century, two mathematicians from England, Gibbs and Heaviside, jointly explored the possibility of combining quaternion calculus and cartesian geometry. The combined product is the evolution of Vector Algebra.
Scalar is a measure of quantity that is determined by magnitude. This is not a moving object like vector. It is static with just the magnitude.
Vector on the other hand is determined by both magnitude and direction. Hence it is also known as directed line segment. We can draw a vector as a straight line with direction and a velocity.
Vector forms a straight line in which the starting point is called the initial point or tail point and the end point is called the tip point or terminal point. Students have to remember these terminologies so that they can understand complex exam questions when it talks about the tail point or the terminal point.
The vector in which there is an option to choose the orgin of the vector is called as free vector. These kind of free vectors are flexible as we can choose & alter the origin as per our need. Hence we can solve mathematical problems using vector algebra easily.
The vector in which there is no option to choose the origin of the vector is called as Localised Vector.
These are two vectors that have same initial point and are called as co-initial vector. These are vectors that start from the same point and then move in same or different directions. Students have to note the initial word in this type of vector that will give a hint that among these kinds of vectors the initial point is the common one.
These are two vectors that have same termination point and are called as coterminal vector. These are two vectors that ends in a same point. These vectors can be in same line or in different line but both converges to same point. Students have to note the terminal word in the vectors as it will give a hint that among these vectors the terminal point is the common one.
These are two vectors that are having the line of action that is parallel to each other. If we take a vector and b vector, if both the a vector and b vector are in same line or parallel lines then it is called as parallel vector. This is similar to two parallel lines, so it will be easy to identify the parallel vectors. Students need to remember the other name of parallel that is collinear which will be used in the exams.
These are two vectors that are in the same plane or parallel to the same plane. The coplanar vector is usually determined in a 3 dimensional scenarios.
Both the vectors need to have same direction and magnitude. It is not necessary that both need to have same starting point and started at sametime. Both should have same direction that could be parallel to each other and same magnitude.
Zero vectors will have zero magnitude and an arbitrary direction
These are two vectors which have same directions. The likeness of vector is determined just by the direction and not by the magnitude. So even a vector with magnitude 10 and vector with magnitude 5 could be like if both the vectors are moving towards same direction.
These are two vectors which have opposite directions. Here again the two vectors need to be moving in opposite direction is the only criteria. It need not move with different magnitude.
We can add two vectors. For instance if a vector acts on an object at x direction with unit of 2 then the object will move from 0,0 to 2,0. Then if another vector acts on an object in y direction with unit of 2 then the object will move from 2,0 to 2,2. So with two vectors acting on an object together will move the object from 0,0 to 2,2. So it will move the object in 45 degree from 0,0 to 2,2.
If we assume the x vector has only 1 unit and y vector has 2 unit, then the object will move in a slanting line instead of a 45 degree line.
In a triangle the sum of vector of all three side in same direction will be zero. Hence this means that if two of the sides are taken in same direction then it will be balanced by the third side acting on the opposite direction.