Let a=-5i+j-3k, b=i+2j-4k and c=((( a b) i) i) i.

Question

Let $\overset{	o }{a}=-5\hat{i}+\hat{j}-3\hat{k},\overset{	o }{b}=\hat{i}+2\hat{j}-4\hat{k}$ and

$\overset{	o }{c}=(((\overset{	o }{a}	imes \overset{	o }{b})	imes \hat{i})	imes \hat{i})	imes \hat{i}$. Then $\vec{c}\cdot (-\hat{i}+\hat{j}+\hat{k})$ is equal to :

Accepted Answer

$\begin{gathered} \vec{a}=-5\cdot \hat{i}+\hat{j}-3\hat{k},\vec{b}=\hat{i}+2\hat{j}-4\hat{k} \ \vec{c}=(((\vec{a}	imes \vec{b})	imes \hat{i})	imes \hat{i})	imes \hat{i} \ =(((\vec{a}\cdot \hat{i})\vec{b}-(\vec{b}\cdot \hat{i})\vec{a})	imes \hat{i})	imes \hat{i} \ =((-5\vec{b}-\vec{a})	imes \hat{i})	imes \hat{i} \end{gathered}$

$\begin{gathered} =((-11\hat{j}+23\hat{k})	imes \hat{i})	imes \hat{i} \ =(11\hat{k}+23\hat{j})	imes \hat{i} \ =(11\hat{j}-23\hat{k}) \end{gathered}$

$\begin{gathered} \vec{c}\cdot (-\hat{i}+\hat{j}+\hat{k})=0+11-23 \ =-12 \end{gathered}$

Solutions · 1