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Think of a screw-thread, threaded just like a screw that you might use to screw a hook into a piece of wood. In the US, all woodscrews are manufactured with what's called a "right-hand thread". That means you turn it right to go into the wood, and you turn it left to bring it out of the wood. Now keep that 'right-hand thread' in the back of your mind, and we'll look at a vector cross-product. A cross-product is the new vector you get when you operate on two vectors that you already have. You obviously know the directions of the vectors that you already have, and you're asking "What is the direction of the new vector ?". Well, call the first two vectors 'A' and 'B'. If you do the cross-product (A x B), think of that right-handed screwthread rotating from the 'A' direction to the 'B' direction. What direction did the right-hand thread advance ? That's the direction of the cross-product ! Can you picture the three-dimensional Cartesian coordinate system ? Down at the origin, where the three axes come together, if you draw three little tiny vectors down on the three axes, you'll notice that ( x cross y = z ). This will help you a lot if you ever have to draw the axes properly on a blank sheet of paper. Notice that (B x A) goes in the opposite direction of (A x B), because when you turn a right-hand thread the other way, the screw advances oppositely. Another contributor may improve this answer by describing the "Right Hand Rule", which is another, maybe better, way to get the direction of the cross product. If he is not a total genius at descriptive language, it will confuse you.
What else can I help you with?
What does the cross product represent in vector algebra?
The cross product in vector algebra represents a new vector that is perpendicular to the two original vectors being multiplied. It is used to find the direction of a vector resulting from the multiplication of two vectors.
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 Poynting vector at this time and position, and how can I find its x-component?
The Poynting vector represents the direction and magnitude of electromagnetic energy flow at a specific time and position. To find its x-component, you can use the formula Poynting vector E x B, where E is the electric field and B is the magnetic field. Calculate the cross product of the electric and magnetic fields to determine the x-component of the Poynting vector.
How to find the direction of a vector?
To find the direction of a vector, you can use trigonometry. First, calculate the angle the vector makes with the positive x-axis. This angle is called the direction angle. You can use the arctangent function to find this angle. The direction of the vector is then given by the direction angle measured counterclockwise from the positive x-axis.
How can one determine the direction of a vector using the keyword "how to find vector direction"?
To determine the direction of a vector using the keyword "how to find vector direction," one can follow these steps: Identify the components of the vector in terms of its magnitude and direction. Use trigonometric functions such as sine and cosine to calculate the angle of the vector with respect to a reference axis. Express the direction of the vector using the angle calculated in step 2, typically in terms of degrees or radians.
What does the cross product represent in vector algebra?
The cross product in vector algebra represents a new vector that is perpendicular to the two original vectors being multiplied. It is used to find the direction of a vector resulting from the multiplication of two vectors.
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.
How do you do cross products?
You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
How to you find a vector parallel to two given vectors?
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
What is cross in science?
One type of cross is the cross or vector product of a pair of 3D vectors. If there are two unit vectors that are not parallel, their vector product is a vector that is normal to the plane containing the two vectors, so it's a good way to find that plane. In biological science, cross signifies the mating of two genotypes to produce its progeny. It may be among homozygous or heterozygous parents.
What is the Poynting vector at this time and position, and how can I find its x-component?
The Poynting vector represents the direction and magnitude of electromagnetic energy flow at a specific time and position. To find its x-component, you can use the formula Poynting vector E x B, where E is the electric field and B is the magnetic field. Calculate the cross product of the electric and magnetic fields to determine the x-component of the Poynting vector.
How to find the direction of a vector?
To find the direction of a vector, you can use trigonometry. First, calculate the angle the vector makes with the positive x-axis. This angle is called the direction angle. You can use the arctangent function to find this angle. The direction of the vector is then given by the direction angle measured counterclockwise from the positive x-axis.
How can one determine the direction of a vector using the keyword "how to find vector direction"?
To determine the direction of a vector using the keyword "how to find vector direction," one can follow these steps: Identify the components of the vector in terms of its magnitude and direction. Use trigonometric functions such as sine and cosine to calculate the angle of the vector with respect to a reference axis. Express the direction of the vector using the angle calculated in step 2, typically in terms of degrees or radians.
What is the right hand rule used for when determining the direction of the cross product?
The right hand rule is used to determine the direction of the cross product in mathematics and physics. It helps to find the perpendicular direction to two given vectors by using the orientation of the right hand.
How can you find a unit vector in the same direction as the given vector?
Divide the vector by it's length (magnitude).
How to calculate the direction of a vector?
To calculate the direction of a vector, you can use trigonometry. Find the angle the vector makes with the positive x-axis using the arctangent function. This angle represents the direction of the vector in relation to the x-axis.
How to determine the direction of a vector?
To determine the direction of a vector, you can use trigonometry. Find the angle the vector makes with the positive x-axis using the arctangent function. This angle represents the direction of the vector in relation to the x-axis.
