Let a=i+2j+k, b=3(i-j+k).

Question

Let $\overset{	o }{a}=\hat{i}+2\hat{j}+\hat{k},$

$\overset{	o }{b}=3(\hat{i}-\hat{j}+\hat{k})$.

Let $\overset{	o }{c}$ be the vector such that $\overset{	o }{a}	imes \overset{	o }{c}=\overset{	o }{b}$ and $\vec{a}\cdot \vec{c}=3$.

Then $\vec{a}\cdot ((\vec{c}	imes \vec{b})-\vec{b}-\vec{c})$ is equal to :

Accepted Answer

$\begin{gathered} \vec{a}\cdot [(\vec{c}	imes \vec{b})-\vec{b}-\vec{c}] \ \vec{a}\cdot (\vec{c}	imes \vec{b})-\vec{a}\cdot \vec{b}-\vec{a}\cdot \vec{c}\, \end{gathered}$

$\begin{gathered} \vec{a}	imes \vec{c}=\vec{b} \ \Rightarrow (\vec{a}	imes \vec{c})\cdot \vec{b}=\vec{b}\cdot \vec{b}=|\vec{b}{|}^{2}=27 \ \Rightarrow \vec{a}\cdot (\vec{c}	imes \vec{b})=[\vec{a}\, \vec{c}\, \vec{b}]=(\vec{a}	imes \vec{c})\cdot \vec{b}=27\, \end{gathered}$

$\begin{gathered} \vec{a}\cdot \vec{b}=3-6+3=0\, \ \vec{a}\cdot \vec{c}=3\, \end{gathered}$

Solutions · 1