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

Question

Let $\overset{	o }{a}=3\hat{i}-\hat{j}+2\hat{k},\overset{	o \leftarrow }{b}=\overset{	o }{a}	imes (\hat{i}-2\hat{k})$ and $\overset{	o }{c}=\overset{	o }{b}	imes \hat{k}$. Then the projection of $\overset{	o }{c}-2\hat{j}$ on $\vec{a}$ is :

Accepted Answer

$\begin{gathered} \begin{gathered} \quad \overset{	o }{b}=\overset{	o }{a}	imes (\hat{i}-3\hat{k}) \ =|\begin{array}{ccc}\hat{i} \quad \hat{j} \quad \hat{k} \ 3 \quad -1 \quad 2 \ 1 \quad 0 \quad -2\end{array}|=2\hat{i}+8\hat{j}+\hat{k} \ \overset{	o }{c}=\overset{	o }{b}	imes \hat{k}=8\hat{i}-2\hat{j} \ \overset{	o }{c}-2\hat{j}=8\hat{i}-4\hat{j} \ (\hat{i}-2\hat{j})\vec{a} \ \quad (\overset{	o }{c}-2\hat{j})\cdot \hat{a}=\frac{\langle 8,-4,0angle \cdot \langle 3,-1,2angle }{\sqrt{14}} \ =\frac{28}{\sqrt{14}}=2\sqrt{14} \end{gathered} \end{gathered}$

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