The value of [a - b, b - c, c - a],where |a| | vedclass

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(A) The scalar triple product is defined as $[x, y, z] = (x 	imes y) \cdot z$. We need to evaluate $[a - b, b - c, c - a]$. Using the properties of t

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(A) The scalar triple product is defined as $[x, y, z] = (x 	imes y) \cdot z$. We need to evaluate $[a - b, b - c, c - a]$. Using the properties of the scalar triple product,we have: $[a - b, b - c, c - a] = (a - b) \cdot ((b - c) 	imes (c - a))$ $= (a - b) \cdot (b 	imes c - b 	imes a - c 	imes c + c 	imes a)$ Since $c 	imes c = 0$,this simplifies to: $= (a - b) \cdot (b 	imes c - b 	imes a + c 	imes a)$ $= a \cdot (b 	imes c) - a \cdot (b 	imes a) + a \cdot (c 	imes a) - b \cdot (b 	imes c) + b \cdot (b 	imes a) - b \cdot (c 	imes a)$ Using the property that the scalar triple product is zero if any two vectors are identical: $a \cdot (b 	imes a) = [a, b, a] = 0$ $a \cdot (c 	imes a) = [a, c, a] = 0$ $b \cdot (b 	imes c) = [b, b, c] = 0$ $b \cdot (b 	imes a) = [b, b, a] = 0$ Thus,the expression simplifies to: $= [a, b, c] - [b, c, a]$ Since $[a, b, c] = [b, c, a]$,we get: $= [a, b, c] - [a, b, c] = 0$.

The value of $[a - b, b - c, c - a]$,where $|a| = 1, |b| = 5$ and $|c| = 3$,is

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