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Three Dimensional Geometry

121138 If $l, m, n$ are the $DC$ 's of a line, then

l^{2} + m^{2} + n^{2} = 0

l^{2} + m^{2} + n^{2} = 1

l + m + n = 1

l = m = n = 0

Explanation:

B If $1, m, n$ are the direction cosines of a line then,
$l^{2} + m^{2} + n^{2} = 1$

CG PET- 2010

Three Dimensional Geometry

121167 If a line makes $α, β, γ$ with the positive direction of $x, y$ and $z$ -axes respectively. Then, $\cos^{2} α + \cos^{2} β + \cos^{2} γ$ is equal to

\frac{1}{2}

- \frac{1}{2}

3 -1

4 1

Explanation:

D Let, $α, β, γ$ the angles which the line makes with the positive direction at the axes of $x, y$ , and $z$ respectively then $\cos α, \cos β$ and $\cos γ$ are called the direction cosines of the line and these are usually denoted by -
$l = \cos α, m = \cos β, n = \cos γ$
$∴ \cos^{2} α + \cos^{2} β + \cos^{2} γ = l^{2} + m^{2} + n^{2} = 1$

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Three Dimensional Geometry

121138 If $l, m, n$ are the $DC$ 's of a line, then

l^{2} + m^{2} + n^{2} = 0

l^{2} + m^{2} + n^{2} = 1

l + m + n = 1

l = m = n = 0

Explanation:

B If $1, m, n$ are the direction cosines of a line then,
$l^{2} + m^{2} + n^{2} = 1$

CG PET- 2010

Three Dimensional Geometry

121167 If a line makes $α, β, γ$ with the positive direction of $x, y$ and $z$ -axes respectively. Then, $\cos^{2} α + \cos^{2} β + \cos^{2} γ$ is equal to

\frac{1}{2}

- \frac{1}{2}

3 -1

4 1

Explanation:

Manipal UGET-2019

For More Updates join with Us