Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Classical Mechanics (Kibble & Berkshire) · Problem 1.9
Velocity, acceleration and scalar angular velocity — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · vector-algebra-triple-scalar-product
Problem If a 1 = λ 1 i + μ 1 j + ν 1 k \boldsymbol{a}_1 = \lambda_1 \boldsymbol{i} + \mu_1 \boldsymbol{j} + \nu_1 \boldsymbol{k} a 1 = λ 1 i + μ 1 j + ν 1 k a 2 = λ 2 i + μ 2 j + ν 2 k \boldsymbol{a}_2 = \lambda_2 \boldsymbol{i} + \mu_2 \boldsymbol{j} + \nu_2 \boldsymbol{k} a 2 = λ 2 i + μ 2 j + ν 2 k a 3 = λ 3 i + μ 3 j + ν 3 k \boldsymbol{a}_3 = \lambda_3 \boldsymbol{i} + \mu_3 \boldsymbol{j} + \nu_3 \boldsymbol{k} a 3 = λ 3 i + μ 3 j + ν 3 k { i , j , k } \{\boldsymbol{i}, \boldsymbol{j}, \boldsymbol{k}\} { i , j , k } a 1 ⋅ ( a 2 × a 3 ) = ∣ λ 1 μ 1 ν 1 λ 2 μ 2 ν 2 λ 3 μ 3 ν 3 ∣ . \boldsymbol{a}_1 \cdot (\boldsymbol{a}_2 \times \boldsymbol{a}_3) = \begin{vmatrix} \lambda_1 & \mu_1 & \nu_1 \\ \lambda_2 & \mu_2 & \nu_2 \\ \lambda_3 & \mu_3 & \nu_3 \end{vmatrix}. a 1 ⋅ ( a 2 × a 3 ) = λ 1 λ 2 λ 3 μ 1 μ 2 μ 3 ν 1 ν 2 ν 3 . Browse the problem library