- #1
-EquinoX-
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Homework Statement
A = -3i + 4j and B = 2i + 3j
so I want to find AxB
Homework Equations
The Attempt at a Solution
what I got is -9k + 8k, which is -k but the answer solution says it's -17k ?
The cross product of two vectors A and B is a vector that is perpendicular to both A and B and has a magnitude equal to the product of their magnitudes multiplied by the sine of the angle between them.
The cross product of two 3-dimensional vectors A = [a1, a2, a3] and B = [b1, b2, b3] is calculated by taking the determinant of the following matrix:
| i j k |
| a1 a2 a3 |
| b1 b2 b3 |
This results in a vector C = [c1, c2, c3] where c1, c2, and c3 represent the x, y, and z components of the cross product, respectively.
The cross product is important in both mathematics and physics because it allows us to calculate the direction and magnitude of a vector that is perpendicular to two given vectors. This is useful in many applications, such as calculating torque in physics or finding the normal vector to a plane in mathematics.
No, the cross product can only be applied to vectors in 3-dimensional space. This is because the determinant method used to calculate the cross product only works for 3x3 matrices.
The cross product has many real-life applications, such as determining the direction of torque on a spinning object, calculating the force exerted by a magnetic field on a current-carrying wire, and finding the direction of the normal force on a surface. It is also used in computer graphics to calculate the direction of reflected light on a 3D object.