Physics
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Dot Product and Cross Product
11
⚡ Quick Summary
The dot product (A · B) gives a scalar, while the cross product (A x B) gives a vector. The dot product is related to the angle between the vectors and the cross product is perpendicular to both vectors.
A ⋅ B = A_x * B_x + A_y * B_y + A_z * B_z
B × C = (B_y * C_z - B_z * C_y)i + (B_z * C_x - B_x * C_z)j + (B_x * C_y - B_y * C_x)k
The text demonstrates the calculation of A ⋅ (B × C) where A, B, and C are vectors expressed in terms of i, j, and k components. It utilizes the properties of the cross product i × j = k, j × k = i, k × i = j, and i × i = j × j = k × k = 0. Then the dot product is calculated by multiplying corresponding components and summing the results.