Direction Ratios

Q. If the direction cosines of a line are l, m and n and the direction ratios of the same line are a, b & c then which of the following is always correct ?

1. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=1$
2. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=2$
3. $\frac{l}{a}=\frac{m}{b}=\frac{n}{c}=K$, where $‘K^{\prime }$ is any constant real number.
4. None of these

Q. If the direction ratios of a line are (1, 1, 2), then find the direction cosines of the line.

1. (1, 1, 2)
2. $\left(0,\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)$
3. $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}}\right)$
4. $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)$

Q. If 1, 2, 1 are the direction ratios of a line then which of the following could be direction cosines of this line?

1. $2\sqrt{\frac{1}{6}},\sqrt{\frac{1}{6}},\sqrt{\frac{1}{6}}$
2. $\sqrt{\frac{1}{6}},2.\sqrt{\frac{1}{6}},\sqrt{\frac{1}{6}}$
3. $\sqrt{\frac{1}{6}},\sqrt{\frac{1}{6}},2.\sqrt{\frac{1}{6}}$
4. None of these