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AakashPandita
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how is î x jcap = kcap? Please help!
AakashPandita said:yes. a x b = absinθ
That's not the definition, and that equality isn't correct. You may be thinking of the result ##\left|\mathbf a\times\mathbf b\right|=|\mathbf a||\mathbf b|\sin\theta##, where ##\theta## is the angle between the two vectors.AakashPandita said:yes. a x b = absinθ
Fredrik said:That's not the definition, and that equality isn't correct. You may be thinking of the result ##\mathbf a\times\mathbf b=|\mathbf a||\mathbf b|\sin\theta##, where ##\theta## is the angle between the two vectors.
LOL, yes I know. That's why I started typing that. Somehow I forgot to type the absolute value symbols on the left. I will edit my post.pwsnafu said:Again LHS is a vector, RHS is a scalar.
The symbol "î x jcap = kcap" represents the cross product of the unit vector î and the unit vector jcap, which results in the unit vector kcap. This is a mathematical operation that is commonly used in physics and engineering to calculate the direction of a vector that is perpendicular to two given vectors.
To calculate the cross product of two vectors, you first need to determine the components of the two vectors in the x, y, and z directions. Then, using the following formula, you can find the components of the resulting vector:
A x B = (AyBz - AzBy) î + (AzBx - AxBz) jcap + (AxBy - AyBx) kcap.
The cross product of two unit vectors always results in a vector with a magnitude of 1, or a unit vector. This is because the cross product is calculated by finding the perpendicular vector to the two given vectors, and since unit vectors represent direction only, the resulting vector will also only have a direction and no magnitude.
The unit vector kcap represents the direction of the resulting vector in the z direction. This is because the cross product of two vectors will always result in a vector that is perpendicular to both of the given vectors, and since the unit vector kcap points in the positive z direction, it shows the direction of the resulting vector in relation to the two given vectors.
The cross product is commonly used in physics and engineering to calculate the direction of forces, torque, and magnetic fields. It is also used in 3D graphics and computer programming to determine the orientation of objects in 3D space. Additionally, it has applications in calculating the area of a parallelogram or triangle formed by two given vectors.