Question

If $a=j-k$ and $c=i-j-k$. then the vector b satisfying $a\times b+c=0$ and $a·b=3$?

• A. $-i+j–2k$
• B. $2i–j+2k$
• C. $i–j–2k$
• D. $i+i–2k$

Answer 1

The correct option is A

$-i+j–2k$

Explanation for the correct option:

Find vector $b$:

Given, $a=j-k$ and $c=i-j-k$

$a\times b+c=0$ and $a·b=3$

Consider, $a\times b+c=0$

$\Rightarrow$ $a\times (a\times b)+a\times c=0$

$\Rightarrow$$(a·b)a–(a·a)b+a\times c=0$

$\Rightarrow$ $3a–2b+a\times c=0$

$\Rightarrow$ $2b=3a+a\times c$

$\Rightarrow$ $\begin{array}{rcl}2b& =& 3j–3k-2i–j–k\\ & =& -2i+2j-4k\end{array}$

$\mathbf{\therefore }\mathit{b}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathit{i}\mathbf{}\mathbf{+}\mathbf{}\mathit{j}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathit{k}$

Hence, Option ‘A’ is Correct.