TS EAMCET · Maths · Three Dimensional Geometry
If \(\vec{a}=\hat{i}-\hat{j}+3 \hat{k}, \hat{c}=-\hat{k}\) are position vectors of two points and \(\vec{b}=2 \hat{i}-\hat{j}+\lambda \hat{k}, \hat{d}=\hat{i}+2 \hat{j}-\hat{k}\) are two vectors, then the lines \(\vec{r}=\vec{a}+t \vec{b}, \vec{r}=\vec{c}+s \vec{d}\) are
- A skew line when \(\lambda=\frac{19}{3}\)
- B coplanar \(\forall \lambda \in \mathbf{R}\)
- C skew lines when \(\lambda \neq \frac{19}{3}\)
- D coplanar when \(\lambda \neq \frac{19}{3}\)
Answer & Solution
Correct Answer
(C) skew lines when \(\lambda \neq \frac{19}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \vec{a}=\hat{i}-\hat{j}+3 \hat{k} \\ \vec{b}= & 2 \hat{i}-\hat{j}+\lambda \hat{k} \\ \vec{c}= & -\hat{k} \text { and } \vec{d}=\hat{i}+2 \hat{j}-\hat{k}\end{aligned}\) The lines \(\vec{r}=\vec{a}+t \vec{b}, \vec{r}=\vec{c}+s \vec{d}\) are coplanar if…
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