Mathematics - Vector Question with Solution | TestHub

$\overline{\mathrm{a}}\times \overline{\mathrm{b}}+\overline{\mathrm{b}}=\overline{\mathrm{c}}\times \overline{\mathrm{a}}+\overline{\mathrm{b}}\times \overline{\mathrm{c}}$ taking dot product with$\overline{\mathrm{a}}$ and$\overline{\mathrm{b}}$ respectively$\overline{\mathrm{a}}.\overline{\mathrm{b}}=[\overline{\mathrm{a}}\overline{\mathrm{b}}\overline{\mathrm{c}}]$$\&|\overline{\mathrm{b}}{|}^2=[\overline{\mathrm{a}}\overline{\mathrm{b}}\overline{\mathrm{c}}]$ Let$|\overline{\mathrm{a}}|=|\overline{\mathrm{b}}|=\mathrm{k}$$\Rightarrow [\overline{\mathrm{a}}\overline{\mathrm{b}}\overline{\mathrm{c}}]={\mathrm{k}}^2\cos \theta$ \&$[\overline{\mathrm{a}}\overline{\mathrm{b}}\overline{\mathrm{c}}]={\mathrm{k}}^2$$\Rightarrow \cos \theta =1$ where$\theta ={\overline{\mathrm{a}}}^{\wedge }\overline{\mathrm{b}}$$\Rightarrow \overline{\mathrm{a}}=\overline{\mathrm{b}}$ putting in (i)$\overline{\mathrm{a}}=\overline{\mathrm{c}}\times \overline{\mathrm{a}}+\overline{\mathrm{a}}\times \overline{\mathrm{c}}$$\Rightarrow \overline{\mathrm{a}}=\overline{0}$$\Rightarrow \overline{\mathrm{b}}=\overline{0}$ and$\overline{\mathrm{c}}$ can be any general vector Passages Paragraph for Question 17 and 18 Given$\vec{a}=\hat{i}+2\hat{j}-3\hat{k},\vec{b}=2\hat{i}-\hat{j}+\hat{k}$ and$L$ be a line whose equation is$\vec{r}\times \vec{b}=\vec{a}\times \vec{b}$.$\vec{a}=\hat{i}+2\hat{j}-3\hat{k},\vec{b}=2\hat{i}-\hat{j}+\hat{k}$$L$$\vec{r}\times \vec{b}=\vec{a}\times \vec{b}$