let a= 2i+k, b= i+j+k, c= 4i-3j+7k, be three vectors. find a vector r which satisfies rb=cb and r.a=0.
Let $\vec{a}=2 \hat{i}+ \hat{k}$ , $\vec{b}= \hat{i}+ \hat{j}+ \hat{k}$ and $\vec{c}=4 \hat{i}-3 \hat{j}+7 \hat{k}$. Find a vector $\vec{r} $ which satisfies $\vec{r} \cdot \vec{b}=\vec{c} \cdot \vec{b}$ and $\vec{r} \cdot \vec{a}=0$
Is is not possible to get a unique vector here? I am only able to see two equations but there are three unknowns $(\vec{r}=p\hat{i}+ q\hat{j}+ r\hat{k})$
It is not possible to have a unique vector.
If $\vec{r}$ is solution than $\alpha\vec{r}$ is also solution, for any real $\alpha$.You can try to find one for which $|\vec{r}|=1$