## Parallelogram Law of Vector Addition Class 11

Answer: According to the parallelogram law of vector addition, if two vectors ( vec{a} ) and ( vec{b} ) represent two sides of a parallelogram in size and direction, then their sum ( vec{a} ) + ( vec{b} ) = the diagonal of the parallelogram passing through its common point in size and direction. To find the answer, consider two vectors shown below ( vec{a} ) and ( vec{b} ) as the two adjacent sides of a parallelogram in their size and direction. The steps of the parallelogram law of vector addition are: For any two vectors ( vec{a} ) and ( vec{b} ), In mathematics, the parallelogram law is the basic law that belongs to elementary geometry. This law is also known as parallelogram identity. In this article, we will examine in detail the definition of a parallelogram law, a proof, and a parallelogram law of vectors. This is also true because it is a null vector since the start and end points coincide, as shown below: Also, for each vector ( vec{a} ) ( vec{a} ) + ( vec{0} ) = ( vec{0} ) + ( vec{a} ) = ( vec{a} ) Note: Vectors are shown in bold. Scalars are represented in the normal type Their sum ( vec{a} ) + ( vec{b} ) is represented in size and direction by the diagonal of the parallelogram by its commonality. This is the parallelogram law of vector addition. Answer: The statement of the vector addition law of the parallelogram states that if the two vectors happen to be adjacent sides of a parallelogram, the result of two vectors is represented by a vector. In addition, this vector happens to be a diagonal whose passage occurs through the point of contact of two vectors. Therefore, applying the triangular distribution of vector addition ( vec{AC`} ) = ( vec{AB} ) + ( vec{BC`} ) = ( vec{AB} ) + ( – ( ( ( vec{BC`} )) = ( vec{a} ) – ( vec{b} ) The vector ( vec{AC`} ) represents the difference between the vectors ( vec{a} ) and ( vec{b} ). For example, OA is the given vector.

We need to find its component along the horizontal axis. Let`s call it the x-axis. We deposit a vertical AB of A on the x-axis. The length OB is the component of the OA along the x-axis. If OA forms the angle p with the horizontal axis, then in the triangle OAB is ob/OA = Cos P or OB = OA Cos P. The vectors ( vec{a} ), ( vec{b} ) and ( vec{c} ) are represented by ( vec{PQ} ), ( vec{QR} ) and ( vec{RS} , respectively. Now ( vec{a} ) + ( vec{b} ) = ( vec{PQ} ) + ( vec{QR} ) = ( vec{PR} ) Let, ( vec{AB} ) = ( vec{a} ) and ( vec{BC} ) = ( vec{b} ). If we now consider the triangle ABC and use the triangular distribution of vector addition, we have ( vec{AC} ) = ( vec{a} ) + ( vec{b} ) Normally, we solve the vector into components along components perpendicular to each other. Answer: If two force vectors are perpendicular to each other, their resulting vector is drawn in such a way that the formation of a right triangle takes place. In other words, the resulting vector happens to be the hypotenuse of the triangle. The parallelogram law of vector addition is a method used to find the sum of two vectors in vector theory. We study two laws for vector addition – the triangular law of vector addition and the parallelogram law of vector addition.

The parallelogram law of vector addition is used to add two vectors when the vectors to be added form the two adjacent sides of a parallelogram by connecting the tails of the two vectors. Then the sum of the two vectors is given by the diagonal of the parallelogram. Note: The associative property of vector addition allows us to write the sum of the three vectors ( vec{a} ), ( vec{b} ) and ( vec{c} ) without using parentheses: ( vec{a} ) + ( vec{b} ) + ( vec{c} ) Answer: The commutative property of vector addition indicates that for any two vectors ( vec{a} ) and ( vec{b} ), ( vec{a} ) + ( vec{b} ) = ( vec{b} ) + ( vec{a} ) To Change the Component of a Vector Along a Given Axis If two Vectors can be represented by the two adjacent sides (both in size and direction) of a parallelogram drawn from a point, then their resulting sum vector is entirely represented by the diagonal of the parallelogram drawn from the same point. We know that in a parallelogram the adjacent angles are complementary. In this article, we will focus on vector addition. We learn the triangular law and the law of parallelogram as well as the commutative and associative properties of vector addition. Now the net speed of the fish is the sum of the two speeds – the speed of the fish and the speed of the river flow, which will be a different speed. As a result, the fish moves along another vector, which is the sum of these two velocities. Now, to determine net velocity, we can consider these two vectors as adjacent sides of a parallelogram and use the parallelogram law of vector addition to determine the resulting sum vector. To prove the formula for the parallelogram law, consider two vectors P and Q, represented by the two adjacent sides OB and OA of the parallelogram OBCA. The angle between the two vectors is θ. The sum of these two vectors is represented by the diagonal drawn from the same vertex O of the parallelogram, the sum vector R, which forms an angle β with the vector P.

The zero vector is also known as additive identity for vector addition. Answer: The size of a vector refers to the length of the vector.