Question

a x (b x C) = (a.c)b -(a.b)c​

Answer 1

Answer:

take

A= Ax i+Ay j+Az k

B= Bx i+By j+Bz k

C= Cx i+Cy j+Cz k

Now start with either L HS or R HS

Lets start with L.H.S

L.H.S = (A x(B x C))

First we will solve for (B x C)

(B x C) = ( ByCz - BzCy)i +(BzCx - BxCz)j+(BxCy - ByCx)k

Now we will solve for (A x(B x C))

(A x(B x C)) = (AyBxCy-AyByCx-AzBzCx+AzBxCz)i+(AzByCz-AzBzCy-AxBxCy+AxByCx)j+(AxBzCx-AxBxCz-AyByCz+AyBzCy)k ——-(1)

Now we will solve for R.H.S

R.H.S =B(A.C)-C(A.B)

=B.( AxCx +AyCy+AzCz )-C.(AxBx+AyBy+AzBz)

=(AyBxCy-AyByCx-AzBzCx+AzBxCz)i+(AzByCz-AzBzCy-AxBxCy+AxByCx)j+(AxBzCx-AxBxCz-AyByCz+AyBzCy)k —-(2)

Since equation 1 = equation 2

hence L.H.S =R.H.S

Step-by-step explanation:

thank you ❤️...

Answer 2

Answer:

a×(b×c) = (a.c) b - (a.b) c

ab×ac×bc = ab×ac×bc - ab×ac×bc

ab×ac×bc + ab×ac×bc= ab×ac×bc

2ab×2ac×2bc = ab×ac×bc

2(ab×ac×bc) = ab×ac×bc

2 = ab×ac×bc/

ab×ac×bc

2 = 1

Ans (2)

Therefore, a×(b×c) = (a.c) b - (a.b) c = 2

Step-by-step explanation:

Hope it helps you