TS EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the supporting line of the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) are
- A \(\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right)\)
- B \(\left(\frac{1}{2}, \frac{1}{2},-1\right)\)
- C \(\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right)\)
- D \(\left(\frac{-1}{2}, \frac{-1}{2},-1\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{-2}{\sqrt{6}}\right)\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) Its direction ratios are \(1,1,-2\). Hence, its direction cosines are given by \(\frac{1}{\sqrt{1+1+4}}\),…
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