TS EAMCET · Maths · Three Dimensional Geometry
For non-coplanar vectors \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\), if the point of intersection of the line \(\mathbf{r}=\mathbf{a}+t(\mathbf{b}-\mathbf{c})\) and the plane \(\mathbf{r}=\mathbf{b}+\mathbf{c}+x(\mathbf{a}-\mathbf{b})+y(\mathbf{c}+\mathbf{a})\) is \(l \mathbf{a}+m \mathbf{b}+n \mathbf{c}\), then \(3 l+4 m+2 n=\)
- A 0
- B \(\frac{1}{2}\)
- C 2
- D 1
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
We have, Equation of plane \(\mathbf{r}=\mathbf{b}+\mathbf{c}+x(\mathbf{a}-\mathbf{b})+y(\mathbf{c}+\mathbf{a})\) \(=(1-x) \mathbf{b}+(1+y) \mathbf{c}+(x+y) \mathbf{a}\) \(\ldots(i)\) And equation of line \(\mathbf{r}=\mathbf{a}+t(\mathbf{b}-\mathbf{c})\) \(\ldots(ii)\) From…
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