If
A = i +3j -2K and B=4i-2j+4k
Find (2A+B).(A-2B)

GIVEN :

a = 1/√10 ( 3i + k) and

b = 1/7 ( 2i + 3j - 6k)

TO FIND :

( 2a- b) . [ ( a x b ) x ( a + 2b)]

SOLUTION :

◆Going with the equation given,

( 2a - b) . [ ( a x b ) x ( a + 2b)]

= (2a - b) [( a×b×a) + 2(a×b)×b]

◆BAC - CAB RULE,

A×B×C = B( A.B ) - C(A.B )

= (2a- b ) [ (b (a.a ) - a (a.b ) + 2b ( a.b) -2b (a.b]

Solving further

= (2a - b )(b - 2a)

= -4a.a -b.b

=-5.

( 2 - b) . [ ( a x b ) x ( a + 2b)] = -5

Hoped I helped