In this video in Hindi we find out the magnitude and the direction of a vector. This is the solution of Example 07 of Chapter 2 -" PHYSICS AND MATHEMATICS" from Concepts of Physics by H C Verma. To find out the direction of the cross product we use right hand rule. The magnitude of the cross product is the product of the magnitudes of the two vectors and the sine of the angle between those two vectors. We can also say, for the intuition of the cross product, that the cross product is equal to the area vector of the parallelogram whose two adjacent sides are represented by those two vectors whose cross product we are going to find out. It is a very important topic in Physics and for esp. students of class 11 and class 12 who aspire to appear in IIT JEE. "Concepts of Physics" by H C Verma is one of the most recommended books in Physics for the preparation of IIT JEE and other competitive examinations. This chapter on "Vectors" is the founding block in Physics. Understanding Physics without the knowledge is impossible.
Other Relevant Topics :-
Vector Quantity :- A vector quantity has its magnitude along with its direction. So we choose a figure which can depict its magnitude as well as its direction. A vector quantity is represented by an arrow, whereas, the direction of propagation of that arrow gives the direction of that vector quantity and the length of that arrow gives us the magnitude of that vector.
Collinear vectors :- Vector quantities act along the same line or parallel lines are called collinear vectors. When those have the same direction, they are called the parallel vectors and when their directions are opposite those are called anti-parallel vectors.
scalar multiplication of a vector : - When we multiply a scalar quantity or a number with a vector quantity we multiply that with the magnitude of that vector and we leave the direction of that vector quantity intact, because multiplying a number with any direction is meaningless.
Unit Vector :- A unit vector along any direction is nothing but the direction of a vector acting along that direction. In other words you can say that a unit vector along any direction is the vector with magnitude 1 (unit) and with that direction. If we divide a vector by its magnitude we get a unit vector along the direction of that vector. Similarly, if we multiply a magnitude and a unit vector, we will have a vector with that magnitude and with the direction same as that of the unit vector.
Magnitude of the resultant vector :- The square of the magnitude of the resultant vector is the sum of the square of the magnitudes of the individual vectors added with the twice of the product of the magnitudes of the individual vectors times the cosine of the angle between them.
Vector Addition :- The process of vector addition gives us the resultant vector yielded by two or more vectors, i.e., the the net vector due to two or more vectors. There are two ways to add two vectors. First is the 'Triangle rule' where we join the head of the first vector and the tail of the second vector and so on and then we create the resultant vector by joining the tail of the first vector and the head of the last vector. Second rule is 'Parallelogram Rule' where we can add only two vectors. In this process we join the tails of two vectors and then we draw a parallelogram drawing parallel lines with the direction of the vectors and then produce a vector joining the initial point and the opposite vertex of that parallelogram.
Vector subtraction :- Vector subtraction is a special kind of vector addition. Vector A - Vector B can be considered as Vector A + (- Vector B). So to do so we have to, at first, negate Vector B and then we have to do vector addition operation on Vector A and negative of Vector B.
Resolving a Vector :- When a vector is resolved into its components on two perpendicular axes whereas the vector makes an angle θ with one of the axes, one of the component becomes ( Magnitude of the vector ) X sine θ and the other one becomes ( Magnitude of the vector ) X cosine θ.
Vector Representation :- If î is the unit vector along X axis and ĵ is the unit vector along Y axis and the tail of the vector is at the origin and the head of that vector is at (x, y), the vector can be represented as x î + y ĵ . Similarly, in 2 D rectangular x - y coordinate space a vector can be represented as x î + y ĵ + z k , where k is the unit vector along Z axis.
To find the magnitude and the direction of a vector represented in î - ĵ notation i.e., in the notation of unit vectors along two perpendicular axes:- The magnitude can be found out with Pythagorean theorem and the relative direction with simple trigonometry.
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