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For any vectors a, b, and c, prove thata X (b X c) = (a*c)b - (a*b)c

Question

For any vectors a, b, and c, prove that

a X (b X c) = (a*c)b - (a*b)c

check_circleAnswer
Step 1

Calculation:

Let us assume that 

a=ai+ai+ak.b=&i+bzj+b,k mdc=qi+cj+ck
and
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a=ai+ai+ak.b=&i+bzj+b,k mdc=qi+cj+ck and

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Step 2
j
k
bxc= b2
b-Σ-b,c,i
C3
i
j
ΕΣ((-b)-a,6,9- b3)
x(bxc) =
2
ac=c1+a2+3
ab=ab+azb2+3
(a-c)b-(a-b)c =(ac1+acz+agcz}{&i+bj+bk)-(qb1 + a_b» +azc3}Gi+cj+cgk}
-X(a2 c2-b)-a,b,-4¢3)i
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j k bxc= b2 b-Σ-b,c,i C3 i j ΕΣ((-b)-a,6,9- b3) x(bxc) = 2 ac=c1+a2+3 ab=ab+azb2+3 (a-c)b-(a-b)c =(ac1+acz+agcz}{&i+bj+bk)-(qb1 + a_b» +azc3}Gi+cj+cgk} -X(a2 c2-b)-a,b,-4¢3)i

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