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Okokya
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Homework Statement
Vectors A and B both have magnitude M. Joined at the tails, they create a 30' angle. What is A x B in terms of M?
Homework Equations
The Attempt at a Solution
0? OR M^2? Sqrt(3)M/3?
samnorris93 said:Remember that the cross product of two vectors is related to their magnitudes and the sine of the angle between them. Do you remember this?
If they were parallel, the answer would be zero, since the cross product gives you the perpendicular component of one vector along the other. If they were perpendicular, the answer would be M^2.
Okokya said:So for theta 30', ab sin 30 = (M^2)/2 ?
The cross product of two vectors of the same magnitude is a mathematical operation that results in a third vector perpendicular to both of the original vectors. It is also known as the vector product and is denoted by the symbol "×".
The cross product of two vectors of the same magnitude is calculated using the following formula:
A × B = (A_{y}B_{z} - A_{z}B_{y})i + (A_{z}B_{x} - A_{x}B_{z})j + (A_{x}B_{y} - A_{y}B_{x})k
where A and B are the two vectors and i, j, and k are unit vectors along the x, y, and z directions, respectively.
The cross product of two vectors of the same magnitude has several physical significances, such as determining the torque on a rotating object, the direction of magnetic fields, and the angular momentum of a system. It is also used in vector calculus and electromagnetism.
Yes, the cross product of two vectors of the same magnitude can be negative. The sign of the cross product depends on the angle between the two vectors. If the angle is greater than 90 degrees, the cross product will be negative, and if the angle is less than 90 degrees, the cross product will be positive.
The direction of the cross product of two vectors of the same magnitude is determined using the right-hand rule. If the fingers of the right hand are curled in the direction of the first vector, and then the fingers are extended towards the second vector, the thumb will point in the direction of the cross product vector. Alternatively, the direction can also be determined using the cross product formula where the first vector is crossed with the second vector.