If a=2i^+3j^-k^,b=-i^+2j-4k^and c=i^+j^+k^,then what is the value of (a→×b→).(a→×c→)?
47
74
-74
None of these
Step1. Find the value of (a→×b→) and (a→×c→):
Given that a=2i^+3j^-k^,b=-i^+2j-4k^ and c=i^+j^+k^,
Now, (a→×b→)=i^j^k^23-1-12-4
=i^(-12+2)-j(^-8-1)+k^(4+3)=-10i^+9j^+7k^
Now, (a→×c→)=i^j^k^23-1111
=i^(3+1)-j(^2+1)+k^(2-3)=4i^-3j^-k^
Step2. Find the value of (a→×b→).(a→×c→):
(a→×b→).(a→×c→)=(-10i^+9j^+7k^).(4i^-3j^-k^)
=-10×4+9×-3+7×-1=-40-27-7=-74
Hence, the correct option is C.