121138
If \(l, \mathrm{~m}, \mathrm{n}\) are the \(\mathrm{DC}\) 's of a line, then
1 \(l^2+m^2+n^2=0\)
2 \(l^2+m^2+n^2=1\)
3 \(l+\mathrm{m}+\mathrm{n}=1\)
4 \(l=\mathrm{m}=\mathrm{n}=0\)
Explanation:
B If \(1, \mathrm{~m}, \mathrm{n}\) are the direction cosines of a line then, \(l^2+\mathrm{m}^2+\mathrm{n}^2=1\)
CG PET- 2010
Three Dimensional Geometry
121167
If a line makes \(\alpha, \beta, \gamma\) with the positive direction of \(x, y\) and \(z\)-axes respectively. Then, \(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma\) is equal to
1 \(\frac{1}{2}\)
2 \(-\frac{1}{2}\)
3 -1
4 1
Explanation:
D Let, \(\alpha, \beta, \gamma\) the angles which the line makes with the positive direction at the axes of \(\mathrm{x}, \mathrm{y}\), and \(\mathrm{z}\) respectively then \(\cos \alpha, \cos \beta\) and \(\cos \gamma\) are called the direction cosines of the line and these are usually denoted by - \(l=\cos \alpha, \mathrm{m}=\cos \beta, \mathrm{n}=\cos \gamma\) \(\therefore \quad \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=l^2+\mathrm{m}^2+\mathrm{n}^2=1\)
121138
If \(l, \mathrm{~m}, \mathrm{n}\) are the \(\mathrm{DC}\) 's of a line, then
1 \(l^2+m^2+n^2=0\)
2 \(l^2+m^2+n^2=1\)
3 \(l+\mathrm{m}+\mathrm{n}=1\)
4 \(l=\mathrm{m}=\mathrm{n}=0\)
Explanation:
B If \(1, \mathrm{~m}, \mathrm{n}\) are the direction cosines of a line then, \(l^2+\mathrm{m}^2+\mathrm{n}^2=1\)
CG PET- 2010
Three Dimensional Geometry
121167
If a line makes \(\alpha, \beta, \gamma\) with the positive direction of \(x, y\) and \(z\)-axes respectively. Then, \(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma\) is equal to
1 \(\frac{1}{2}\)
2 \(-\frac{1}{2}\)
3 -1
4 1
Explanation:
D Let, \(\alpha, \beta, \gamma\) the angles which the line makes with the positive direction at the axes of \(\mathrm{x}, \mathrm{y}\), and \(\mathrm{z}\) respectively then \(\cos \alpha, \cos \beta\) and \(\cos \gamma\) are called the direction cosines of the line and these are usually denoted by - \(l=\cos \alpha, \mathrm{m}=\cos \beta, \mathrm{n}=\cos \gamma\) \(\therefore \quad \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=l^2+\mathrm{m}^2+\mathrm{n}^2=1\)