TS EAMCET · Maths · Three Dimensional Geometry
If the points \(2 \mathbf{a}+3 \mathbf{b}-\mathbf{c}, \mathbf{a}-2 \mathbf{b}+3 \mathbf{c}\), \(3 \mathbf{a}+\lambda \mathbf{b}-2 \mathbf{c}\) and \(\mathbf{a}-6 \mathbf{b}+6 \mathbf{c}\) are coplanar, then the direction cosines of the vector \(\lambda \hat{\mathbf{i}}-2 \lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}\) are
- A \(\frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}, \frac{1}{\sqrt{21}}\)
- B \(-\frac{2}{\sqrt{78}}, \frac{5}{\sqrt{78}}, \frac{7}{\sqrt{78}}\)
- C \(\frac{4}{9}, \frac{8}{9}, \frac{1}{9}\)
- D \(\frac{2}{3},-\frac{2}{3},-\frac{1}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{4}{9}, \frac{8}{9}, \frac{1}{9}\)
Step-by-step Solution
Detailed explanation
We have, \(2 \mathbf{a}+3 \mathbf{b}-\mathbf{c}, \mathbf{a}-2 \mathbf{b}+3 \mathbf{c}, 3 \mathbf{a}+\lambda \mathbf{b}-2 \mathbf{c}\) and \(\mathbf{a}-\mathbf{6 b}+\mathbf{6} \mathbf{c}\) are coplanar.…
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