The constant value ( + ) for which the lines r = 2i + j + k + (i … - Vidyadip

Question

The constant value ($\lambda$ + $\mu$) for which the lines $\vec{r}$ = $2\hat{i}$ + $\hat{j}$ + $\hat{k}$ + $\lambda$($\hat{i} - 2\hat{j}$) and $\vec{r}$ = $\hat{i}$ + $\hat{j}$ - $3\hat{k}$ + $\mu$ ($\hat{j} + 2\hat{k}$) intersect each other, is equal to (where $\lambda$ & $\mu$ are parameters)

✓

Answer

d
If lines $\vec r = (2 + \lambda )\widehat {\rm{i}} + (1 - 2\lambda )\widehat {\rm{j}} + \widehat {\rm{k}}$

and $\overrightarrow r = \widehat i + (1 + \mu )\widehat j + ( - 3 + 2\mu )\widehat k$

intersects each other, then

$2+\lambda=1,1-2 \lambda=1+\mu $ and $ 1=-3+2 \mu$

$\Rightarrow \lambda=-1, \mu=2$

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