Triangle law of vector addition

Vector Addition Vector addition finds its application in physical quantities where vectors are used to represent velocity, displacement, and acceleration. • Adding the vectors geometrically is putting their tails together and thereby constructing a parallelogram. The sum of the vectors is the diagonal of the parallelogram that starts from the intersection of the tails. • Adding vectors algebraically is adding their corresponding components. In this article, let's learn about the addition of vectors, their properties, and various laws with solved examples. 1. 2. 3. 4. 5. 6. 7. 8. What is the Vector Addition? Vectors are represented as a combination of direction and magnitude and are written with an alphabet and an arrow over them (or) with an alphabet written in bold. Two a and b, can be added together using vector addition, and the resultant vector can be written as: a + b. Before learning about the properties of vector addition, we need to know about the conditions that are to be followed while adding vectors. The conditions are as follows: • Vectors can be added only if they are of the same nature. For instance, acceleration should be added with only acceleration and not mass • We cannot add vectors and scalars together Consider two vectors C and D, where, C = C xi + C yj + C zk and D = D xi + D yj + Dzk. Then, the R = C + D = (C x + D x)i + (C y + D y)j + (C z + C z) k Properties of Vector Addition Vector addition is different from algebraic addition. Here are some of t...

Triangle Law of Vector Addition A vector \( \vec \) = the diagonal of the parallelogram through their common point in magnitude and direction. Question 4: What is meant by sum of two vectors? Answer: The sum of two or more vectors is known as the resultant. One can find the resultant of two vectors by using either the triangle method or the parallelogram method. Question 5: What is meant by magnitude of a vector? Answer: The magnitude of a vector refers to the length of the vector. The denotation of magnitude of the vector a is as ∥a∥. Formulas for the magnitude of vectors are available in two and three dimensions. Question 6: Explain the parallelogram law of vector? Answer: The Statement of Parallelogram law of vector addition is that in case the two vectors happen to be the adjacent sides of a parallelogram, then the resultant of two vectors is represented by a vector. Furthermore, this vector happens to be a diagonal whose passing takes place through the point of contact of two vectors. Question 7: What will be the result of two perpendiculars? Answer: When two force vectors are such that they are perpendicular to each other, their resultant vector is drawn so that the formation of a right-angled triangle takes place. In other words, the resultant vector happens to be the hypotenuse of the triangle.

I know this is a trivial question, but I just wanted to clear my doubt. Using the triangle of vector addition, the resultant of two forces $F_1$ and $F_2$ is given by $$\sqrt$$ In this formula, am I supposed to take only the magnitudes of $F_1$ and $F_2$ or am I supposed to include their signs as well? $\begingroup$ You are applying the law of cosines to the sides of a triangle. The magnitude of the forces are all positive.The angle is measured between the two vectors. By the way, the term with the cosine should be negative. Only the components of a vector can be negative, and that's after you define a coordinate system. $\endgroup$ Vectors have no sign See, forces do not have a sign, and for that matter, vectors have no sign. They just have a direction and a magnitude. Their direction is defined using $\phi$ in your equation is the angle between two forces. And the $F_1$ and $F_2$ are the magnitudes of the corresponding forces and magnitudes of vectors are always positive. Your specific doubt We only have to take the magnitude of the forces without sign. But you have to be careful in finding $\cos \phi$. In the example of $F_1= 5 \: \mathrm N$ and $F_2= -10 \: \mathrm N$, the value of $\phi$ is $180^$ or $\pi$ and hence $\cos\phi= -1$. This means that although you will substitute $F_1$ and $F_2$ without sign, still the $2F_1F_2\cos\phi$ term will be negative. Thanks for contributing an answer to Physics Stack Exchange! • Please be sure to answer the question. Provide deta...

If I understand your question correctly, this is a matter of definition. If you are given two vectors $\vec$. Vector $a$ can be thought of as going from point $A$ to $B$. Similarly, vector $b$ is going from $B$ to $C$ and vector $c$ is going from $A$ to $C$. You went from $A$ to $B$ and then from there to $C$. Totally, you went from $A$ to $C$. So, $a$+$b$=$c$ Note- It's not just in the direction of $c$, but is infact equal to $c$ Note we can prove it using physics . let the distance travelled by a particle be $a+b$ according to your figure. But the displacement is $c$ . now the triangle be $90$ at $B$ so we know magnitude if resultant is $\sqrt$ also magnitude of $c$ is $√c^2$ so if we square both we get $a^2+b^2,c^2$ but they are equal according to pythagoras theorem therefore not only resultant vector but magnitude of both vectors is the same. Also alternate way is complete the parallelogram and by parallelogram law of vectors the resultant of adjacent vectors is diagonal . now as |d| which is parallel to $|b|$ are equal hence the result follows .

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- [Instructor] So we have two vectors here, vector A and vector B. And what we're gonna do in this video is think about what it means to add vectors. So for example, how could we think about what does it mean to take vector A and add to that vector B. And as we'll see, we'll get another third vector. And there's two ways that we can think about this visually. One way is to say, all right, if we want start with vector A and then add vector B to it, what we can do, let me take a copy of vector B and put its tail right at the head of vector A. Notice I have not changed the magnitude or the direction of vector B. If I did, I would actually be changing the vector. And when I do it like that, this defines a third vector which can be use the sum of a plus B. And the sum is going to start at the tail of vector A and end at the head of vector B here. So let me draw that. So it would look something like that. And we can call this right over here, vector C. So we could say A plus B is equal to vector C. Now we could have also thought about it the other way around. We could have said, let's start with vector B and then add vector A to that. So I'll start with the tail of vector B and then at the head of vector B, I'm going to put the tail of vector A. So it could look something like that. And then once again, the sum is going to have its tail at our starting point here and its head at our finishing point. Now, another way of thinking about it is we've just constructed a parallelogram ...