The value of i^×(i^×a→)+j^×(j^×a→)+k^×(k^×a→) is :

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

a→

a→×K

−2a→

−a→

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Remember a→×(b→×c→)=b→(a→.c→)−c→(a→.b→) This is called the vector product. Using above, i^×(i^×a→)=i^.(i^.a→)−a→(i^.i^)=i^(i^.a→)−a→ j^×(j^×a→)=j^.(j^.a→)−a→(j^.j^)=j^(j^.a→)−a→ k^×(k^×a→)=k^.(k^.a→)−a→(k^.k^)=k^(k^.a→)−a→ ∴ i^×(i^×a→)+j^.(j^×a→)+k^×(k^×a→) =i^.(i^.a→)+j^.(j^.a→)+k^.(k^.a→)−3a→ ….(i)Since a→=i^ax+j^by+k^az And ax=i^.a→; ay=j^.a→; az=k^.a→ ∴ i^(i^.a→)+j^(j^.a→)+k^(k^.a→)=i^ax+j^ay+k^az=a→ On putting in eq. (i) we get i^×(i^×a→)+j^×(j^×a→)+k^×(k^×a→)=a→−3a→ =−2a→

Watch 3-min video & get full concept clarity