The lines, r _ 1 = i +2 j +3 k + (2 i +3 j +4 k ) and I _ 2 =2 i +3 j +4 k + (3 i +4 j +5…
Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry
The lines,
\(\vec{r}_{1}=\hat{i}+2 \hat{j}+3 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})\)
and \(\overrightarrow{\mathrm{I}}_{2}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}+\mu(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\) are :
\(\vec{r}_{1}=\hat{i}+2 \hat{j}+3 \hat{k}+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})\)
and \(\overrightarrow{\mathrm{I}}_{2}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}+\mu(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})\) are :
- coplanar
- skew
- such that shortest distance between them is 1
- none
Answer
(A) coplanar
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