TS EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the normal to the plane containing the lines having direction ratios \(1,2,1\) and \(4,5,-3\) are
- A \(\frac{-11}{\sqrt{179}}, \frac{7}{\sqrt{179}}, \frac{-3}{\sqrt{179}}\)
- B \(\frac{1}{\sqrt{2}}, 0, \frac{-1}{\sqrt{2}}\)
- C \(\frac{5}{\sqrt{41}}, \frac{-4}{\sqrt{41}}, 0\)
- D \(\frac{2}{\sqrt{5}}, \frac{-1}{\sqrt{5}}, 0\)
Answer & Solution
Correct Answer
(A) \(\frac{-11}{\sqrt{179}}, \frac{7}{\sqrt{179}}, \frac{-3}{\sqrt{179}}\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{b}_1=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{b}_2=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) Normal vector to plane…
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