If a-b-k- then a-b -a-a-b-

Given a=î+ĵ,b=î+k̂ {{ ( a×b )×a}×a}×b ={{(a·a)b (b·a)a}×a}×b ={|a|^2(b×a) (b·a)(a×a)}×b =|a|^2((b×a)×b 0) =|a|^2{ (b·b)a (a·b)b} =2{ 2(î+ĵ) 1(î+k̂) } =2{î+2ĵ k̂ ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Work Done as Dot Product

If a=î+ĵ,b=î+...

Question

If $\to a =^i +^j, \to b =^i +^k,$ then ${{(\to a \times \to b) \times \to a} \times \to a} \times \to b =$

^i +^j +^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 (^i + 2^j -^k)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

-^i +^j +^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^i -^j +^k

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $2 (^i + 2^j -^k)$
$Given →a=^i+^j,→b=^i+^k{{(→a×→b)×→a}×→a}×→b$
$= {{(\to a \cdot \to a) \to b - (\to b \cdot \to a) \to a} \times \to a} \times \to b$
$= {| \to a |^{2} (\to b \times \to a) - (\to b \cdot \to a) (\to a \times \to a)} \times \to b$
$= | \to a |^{2} ((\to b \times \to a) \times \to b - 0)$
$= | \to a |^{2} {(\to b \cdot \to b) \to a - (\to a \cdot \to b) \to b}$
$=2{2(^i+^j)−1(^i+^k)}=2{^i+2^j−^k}$

Suggest Corrections

Similar questions

Q. If

\to a =^i +^j +^k; \to b =^i -^j +^k; \to c =^i +^j -^k

, then

[^i, \to a, \to b]^i + [^j, \to a, \to b,]^j + [^k, \to a, \to b]^k =

Q. If

\to A + \to B

is a unit vector along x - axis and

\to A =^i -^j +^k

, then what is

\to B

Q. If

\to A + \to B

is a unit vector along x - axis and

\to A =^i -^j -^k

, then what is

\to B

Q. If

\to A + \to B

is a unit vector along y - axis and

\to A =^i -^j +^k

, then what is

\to B

Join BYJU'S Learning Program

Explore more

Work Done as Dot Product

Standard XII Physics

Join BYJU'S Learning Program

If →a=^i+^j,→b=^i+^k, then {{(→a×→b)×→a}×→a}×→b=

If $\to a =^i +^j, \to b =^i +^k,$ then ${{(\to a \times \to b) \times \to a} \times \to a} \times \to b =$