91Ó°ÊÓ

Write two different vectors having same magnitude.

Find \(\lambda\) and \(\mu\) if \((2 \hat{i}+6 \hat{j}+27 \hat{k}) \times(\hat{i}+\lambda \hat{j}+\mu \hat{k})=\overrightarrow{0}\).

Find the position vector of a point \(\mathrm{R}\) which divides the line joining two points \(\mathrm{P}\) and Q whose position vectors are \(\hat{i}+2 \hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}+\hat{k}\) respectively, in the ratio \(2: 1\) (i) internally (ii) externally