Question

If $a=i+j+k,a.b=1$ and $a\times b=j-k$, then b =

• A. i
• B. i-j+k
• C. 2j-k
• D. 2

Answer 1

The correct option is A i

Given,

$a=i+j+k$

let $b=xi+yj+zk$

$a\cdot b=1$

$(i+j+k)\cdot (xi+yj+zk)=1$

$x+y+z=1$.......(1)

now,

$a\times b=j-k$

$(i+j+k)\times (xi+yj+zk)=j-k$

$k(y-x)+j(-z+x)+i(z-y)=j-k$

$\Rightarrow y-x=-1,-z+x=1,z-y=0$.......(2)

From (1) and (2), we get,

$x=1,y=0=z$

$\therefore \overrightarrow{b}=i$