Knowee
Questions
Features
Study Tools

Properties of Vector Addition

Question

Properties of Vector Addition

🧐 Not the exact question you are looking for?Go ask a question

Solution

Sure, here are the properties of vector addition:

  1. Commutative Law: The order in which vectors are added does not change the result. If A and B are two vectors, then A + B = B + A.

  2. Associative Law: The way in which vectors are grouped does not change the result. If A, B, and C are three vectors, then (A + B) + C = A + (B + C).

  3. Additive Identity: The zero vector (0) is the additive identity. If A is a vector, then A + 0 = A.

  4. Additive Inverse: Every vector A has an additive inverse -A such that A + (-A) = 0.

  5. Distributive Law: Vector addition is distributive over scalar multiplication. If A and B are vectors and k is a scalar, then k(A + B) = kA + kB.

  6. Distributive Law: Scalar multiplication is distributive over vector addition. If A and B are vectors and k and l are scalars, then (k + l)A = kA + lA.

These properties make vector addition a very useful tool in physics and engineering, among other fields.

This problem has been solved

Similar Questions

Which of the following correctly shows how to add two vectors (adding the blue vector to the red vector)?

Vector addition produces a __________.Select one:a.nothingb.a multidimensional matrixc.scalar quantityd.vector quantity

Let P₂[R]=(a+a₁x+aα₂x² | Q₁ER,I=0,1,2] =Set of all real polynomials in x of degree ≤2 The vector addition is defined by (a + a₁x+a₂x)+(b₂+ b₁x+b₂x²)=(a+b)+(a,+b)x+(a₂+ b₂)x where a, b, ER, i = 0,1,2. Verify all properties of vector addition for real vector space P₂[R].

If vector B is added to vector A, under what condition does the resultant vector A  B havemagnitude A  B ? Under what conditions is the resultant vector equal to zero

In the parallelogram method of vector addition, when a parallelogram is constructed with two vectors as adjacent sides, the shorter diagonal of the parallelogramGroup of answer choicesis the multiplication of the two vectorsis the difference between the two vectorsis the algebraic sum of the magnitudes of the two vectorsis the sum of two the vectorsis the algebraic difference between the magnitudes of the two vectors

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.