Vector Products Simulation
This interactive simulation demonstrates how to calculate the scalar (dot) product and vector (cross) product of two vectors.
Vector a
Vector b
Scalar (Dot) Product
a · b = (ai × bi) + (aj × bj) + (ak × bk)
(3 × -2) + (-4 × 1) + (5 × -3) = -6 - 4 - 15 = -25
Result: a · b = -25
Vector (Cross) Product
a × b = \[\begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_i & a_j & a_k \\ b_i & b_j & b_k \end{vmatrix}\]
i((-4 × -3) - (5 × 1)) - j((3 × -3) - (5 × -2)) + k((3 × 1) - (-4 × -2))
= i(12 - 5) - j(-9 + 10) + k(3 - 8)
= 7i - j - 5k
= i(12 - 5) - j(-9 + 10) + k(3 - 8)
= 7i - j - 5k
Result: a × b = 7i - j - 5k
Note: b × a = -7i + j + 5k
