Question

for what value of lambda are the vectors i +2 lambda j+k and 2i +j -3k perpendicular

Answer 1

Dear student

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{when}\mathrm{two}\mathrm{vectors}\mathrm{are}\perp ,\mathrm{their}\mathrm{dot}\mathrm{product}\mathrm{is}\mathrm{zero}. \\ \mathrm{let}\overrightarrow{\mathrm{a}}=\mathrm{i}+2\mathrm{\lambda j}+\mathrm{k} \\ \mathrm{and}\overrightarrow{\mathrm{b}}=2\mathrm{i}+\mathrm{j}-3\mathrm{k} \\ \mathrm{So},\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}=0 \\ \Rightarrow 2+2\mathrm{\lambda }-3=0 \\ \Rightarrow 2\mathrm{\lambda }=1 \\ \Rightarrow \mathrm{\lambda }=\frac{1}{2} \\ \mathrm{For},\mathrm{\lambda }=\frac{1}{2}\mathrm{the}\mathrm{vectors}\mathrm{are}\perp \end{gathered}$$
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