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Dot product and cross product are used in many cases in physics. Here are some examples:
- Work is sometimes defined as force times distance. However, if the force is not applied in the direction of the movement, the dot product should be used. Note that here - as well as in other cases where the dot product is used - the product is greatest when the angle is zero; also, the result is a scalar, not a vector.
- The cross product is used to define torque (distance from the axis of rotation, times force). In this case, the product is greatest when the two vectors are at right angles. Also - as in any cross product - the result is also a vector.
- Several interactions between electricity and magnetism are defined as cross products.
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Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
How do you multiply vectors in 3D?
To multiply two vectors in 3D, you can use the dot product or the cross product. The dot product results in a scalar quantity, while the cross product produces a new vector that is perpendicular to the original two vectors.
Why you use cosine theta with cross product?
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
Why we use sine angle in cross product while cos angle in dot product?
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
What are the properties of a dot product?
In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually vectors) and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the interpunct "●" that is often used to designate this operation; the alternative name scalar product emphasizes the scalar result, rather than a vector result.The principal use of this product is the inner product in a Euclidean vector space: when two vectors are expressed in an Orthonormal basis, the dot product of their coordinate vectors gives their inner product. For this geometric interpretation, scalars must be taken to be Real. The dot product can be defined in a more general field, for instance the complex number field, but many properties would be different. In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result.
Vector method to find out the acceleration of a particle is -wwrwhere angular velocity is w?
To find the acceleration of a particle using the vector method, you can use the equation a = r x (w x v), where "a" is the acceleration, "r" is the position vector, "w" is the angular velocity vector, and "v" is the velocity vector. The cross product (x) represents the vector cross product. By taking the cross product of the angular velocity vector with the velocity vector and then multiplying the result by the position vector, you can find the acceleration of the particle.
What is the use of dot product in Physics and explain?
Dot Products in Physics denote scalar results fmo vector products, e.g Work = F.D = FDCos(FD) a scalar result from the dot product of two vectors, F Force and D Displacement.
How do you find a normal vector?
A normal vector is a vector that is perpendicular or orthogonal to another vector. That means the angle between them is 90 degrees which also means their dot product if zero. I will denote (a,b) to mean the vector from (0,0) to (a,b) So let' look at the case of a vector in R2 first. To make it general, call the vector, V=(a,b) and to find a vector perpendicular to v, i.e a normal vector, which we call (c,d) we need ac+bd=0 So say (a,b)=(1,0), then (c,d) could equal (0,1) since their dot product is 0 Now say (a,b)=(1,1) we need c=-d so there are an infinite number of vectors that work, say (2,-2) In fact when we had (1,0) we could have pick the vector (0,100) and it is also normal So there is always an infinite number of vectors normal to any other vector. We use the term normal because the vector is perpendicular to a surface. so now we could find a vector in Rn normal to any other. There is another way to do this using the cross product. Given two vectors in a plane, their cross product is a vector normal to that plane. Which one to use? Depends on the context and sometimes both can be used!
How do you find a nonzero vector perpendicular to the vector represented by the point x 7 y -3?
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Find the torque of a force 7i plus 3j-5k about the origin The force acts on a particle whose position vector is you-j plus k?
To calculate the torque, you can use the cross product formula: Torque = r x F, where r is the position vector and F is the force vector. Given r = i - j + k and F = 7i + 3j - 5k, calculate their cross product to find the torque about the origin.
Write a program in C language to find out the dot product of two vector quantities in Cartesian?
#include <stdio.h> #include <ctype.h> #define n[] int main() { int n, result , answer; int a[n], b[n]; printf("Enter number of terms you would like to use :"); scanf("%d", &n); printf("Enter first vector:\n"); scanf("%d", &a[n]); printf("Enter second vector:\n"); scanf("%d", &b[n]); printf("The dot product is \n" ); return 0; }
How do you calculate the projection of a vector onto another vector?
If A and B are two vectors, the projection (C) of A on B is the vector that has the same slope as B with the length:To calculate C use the following property of the dot product:Using the above equation:Multiply and divide by | B | at the same time:In the resulting fraction, the top term is the same as the dot product, hence:To find the length of | C | with an unknown θ, and unknown direction, multiply it with the unit vector B:giving the final formula:taken from: http://en.wikipedia.org/wiki/Vector_projection
