If a and c are unit vectors inclined at 3 with each other and ( a ( b c )) ( a c )=5 , then the value of 5[ a b c ]=

Step-by-step solution

aligned | a |=| c | & =1 a c & =| a || c | 3 & =1 1 1 2 & = 1 2 aligned Now, [ a ( b c )] ( a c )=5 ...[Given] [( a c ) b -( a ~b ) c ]( a c )=5 aligned & [ 1 2 ~b -( a b ) c ] ( a c )=5 & 1 2 ~b ( a c )-( a b ) c ( a c )=5 & ~b ( a c )=10 & [ ~b a c ]=10 & -[ a b c ]=10 & [ a b c ]=-10 & 5[ a b c ]=-50 aligned