Consider the following Assertion (A) and Reas | vedclass

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(B) For Assertion $(A)$: The lines are $\bar{r}=\bar{a}+t\bar{b}$ and $\bar{r}=\bar{b}+s\bar{a}$. These lines pass through points with position vector

Vedclass · Accepted Answer

Both $(A)$ and $(R)$ are true and $(R)$ is not the correct explanation of $(A)$

Vedclass · Answer

(B) For Assertion $(A)$: The lines are $\bar{r}=\bar{a}+t\bar{b}$ and $\bar{r}=\bar{b}+s\bar{a}$. These lines pass through points with position vectors $\bar{a}$ and $\bar{b}$ respectively, and are parallel to vectors $\bar{b}$ and $\bar{a}$. Since both lines pass through the point with position vector $\bar{a}+\bar{b}$ (by setting $t=1$ in the first and $s=1$ in the second), they intersect. Thus, $(A)$ is true.For Reason $(R)$: The shortest distance between two skew lines $\bar{r}=\bar{p}+t\bar{q}$ and $\bar{r}=\bar{c}+s\bar{d}$ is given by the formula $d = \frac{|(\bar{p}-\bar{c}) \cdot (\bar{q} 	imes \bar{d})|}{|\bar{q} 	imes \bar{d}|}$. This is indeed the length of the projection of the vector $(\bar{p}-\bar{c})$ onto the vector $(\bar{q} 	imes \bar{d})$. Thus, $(R)$ is true.However, the intersection of the lines in $(A)$ is a specific property of these lines, while $(R)$ provides a general formula for the shortest distance between skew lines. Therefore, $(R)$ is not the correct explanation for $(A)$.The correct option is $(B)$.

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