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Let x = [x1, x2, ... xk] and y= [y1, y2, ... yk] be the two vectors of length k.
Then we define their sum to be x+y = [x1+y1, x2+y2, ... xk+yk]
In other words, add the corresponding elements in the two vectors.
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What is the difference between vector addition and algebraic addition?
There is no difference between vector addition and algebraic addition. Algebraic Addition applies to vectors and scalars: [a ,A ] + [b, B] = [a+b, A + B]. Algebraic addition handles the scalars a and b the same as the Vectors A and B
What is the physical significance of null vectors?
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
Direction of vector in space is specified by?
It is an integral part of the vector and so is specified by the vector.
The components of a vector or what?
The components of a vector are magnitude and direction.
What is the resultant of a 3 unit vector and 4 unit vector at right angles to each other?
The multiplicative resultant is a three unit vector composed of a vector parallel to the 3 unit vector and a vector parallel to the product of the 3 unit and 4 unit vectors. R = (w4 + v4)(0 +v3) = (w40 - v4.v3) + (w4v3 + 0v4 + v4xv3) R = (0 - 0) + w4v3 + v4xv3 as v4.v3 =0 ( right angles or perpendicular)
Is it necessary that every vector has to obey the law of vector addition?
Yes.
What is the opposite to vector addition?
the opposite to vector addition is vector subtraction.
What is the reverse process of vectors addition?
reverse process of vector addition is vector resolution.
How do you carry out experiment to verify parallelogram law of vector addition?
Using Gravesand's apparatus
What are balenced forces?
Forces acting on a point such that it gives a null vector by vector addition law, then such type of forces are called balanced forces.
Does vector subtraction commutes?
Vector addition is basically similar, with respect to many of its properties, to the addition of real numbers.A + B = B + ASubtraction is the inverse of addition: A - B = A + (-B), where (-B) is the opposite vector to (B).A - B is not usually the same as B - A. Therefore, it is not commutative.However, if you convert it to an addition, you can apply the commutative law: A + (-B) = (-B) + A.
Why is Vector resolution the opposite of vector addition?
Vector addition derives a new vector from two or more vectors, and vector resolution is breaking a vector down into its two or more components.
Can the triangle law of vector addition be used for many vectors?
no because triangle only contain three vectors and if many vector are added then they cant form a triangle
What is the difference between parallelogram law of vector addition n triangle law of vector addition?
There is basically no difference. They are nothing more than 2 different visualizations of how we can graphically add two vectors.strictly if we say there is one and only difference is that---Triangle law of vector addition states that when 2 vectors r acting as the adjacent sides of a triangle taken in order. third side of the triangle will give the magnitude of th resultant 7 direction is in opposite order.Parallelogram law of vector addition states that if 2 vectors r acting as the adjacent sides of a parallelogram, then the diagonal of parallelogram from the point of intersection of two vectors represent their resultant magnitude & direction.
What is the example of head to tail rule?
In addition of vector when vector A whose head is joined to the tail of the vector B and then the tail of the vector A is linked with the tail of the resultant vector and the head of the vector B is joined with the head of the resultant vector..... it means the addition of vectors are also defined the head to tail rule..
Does commutative law applied to the vector subtraction?
No. It is the same as when you subtract normal numbers. a - b is not the same as b - a. However, if you convert the subtraction to an addition, you can use the commutative law - both with normal subtraction and with vector subtraction. That is, a - b, which can be written as a + (-b), is the same as -b + a.
Why the direction of resultant vector in the triangle law of addition is reverse?
In order to bring the system to equilibrium, action and reaction cancel out. The resultant is the reaction.
