Question

(b) (mathbf{u} imes (mathbf{v} + mathbf{w}) = mathbf{u} imes mathbf{v} + mathbf{u} imes mathbf{w}) 57. Vector Product Properties. For any vectors (mathbf{a}), (mathbf{b}) and (mathbf{c} in mathbb{R}^3), and scalars (alpha, eta in mathbb{R}), show that: (a) (mathbf{a} imes mathbf{b} = -mathbf{b} imes mathbf{a}) (c) (mathbf{a} imes (alpha mathbf{b} + eta mathbf{c}) = alpha mathbf{a} imes mathbf{b} + eta mathbf{a} imes mathbf{c}) (b) ((alpha mathbf{a} + eta mathbf{b}) imes mathbf{c} = alpha mathbf{a} imes mathbf{c} + eta mathbf{b} imes mathbf{c}) (d) (mathbf{a} imes mathbf{a} = mathbf{0})

          (b) (mathbf{u} 	imes (mathbf{v} + mathbf{w}) = mathbf{u} 	imes mathbf{v} + mathbf{u} 	imes mathbf{w})
57. Vector Product Properties. For any vectors (mathbf{a}), (mathbf{b}) and (mathbf{c} in mathbb{R}^3), and scalars (alpha, eta in mathbb{R}), show that:
(a) (mathbf{a} 	imes mathbf{b} = -mathbf{b} 	imes mathbf{a})
(c) (mathbf{a} 	imes (alpha mathbf{b} + eta mathbf{c}) = alpha mathbf{a} 	imes mathbf{b} + eta mathbf{a} 	imes mathbf{c})
(b) ((alpha mathbf{a} + eta mathbf{b}) 	imes mathbf{c} = alpha mathbf{a} 	imes mathbf{c} + eta mathbf{b} 	imes mathbf{c})
(d) (mathbf{a} 	imes mathbf{a} = mathbf{0})

(b) (mathbfu imes (mathbfv + mathbfw) = mathbfu imes mathbfv + mathbfu imes mathbfw)
57. Vector Product Properties. For any vectors (mathbfa), (mathbfb) and (mathbfc in mathbbR^3), and scalars (alpha, eta in mathbbR), show that:
(a) (mathbfa imes mathbfb = -mathbfb imes mathbfa)
(c) (mathbfa imes (alpha mathbfb + eta mathbfc) = alpha mathbfa imes mathbfb + eta mathbfa imes mathbfc)
(b) ((alpha mathbfa + eta mathbfb) imes mathbfc = alpha mathbfa imes mathbfc + eta mathbfb imes mathbfc)
(d) (mathbfa imes mathbfa = mathbf0)

Added by Carla K.

Question

Please give Ace some feedback