Class 12 Three Dimensional Geometry Quiz 1

1. Angle $ \theta $ between two lines is given by...

2. Given skew lines $ \vec{r} = \vec{a_1} + \lambda \vec{b_1} \ and \ \vec{r} = \vec{a_2} + \lambda \vec{b_2}$, the shortest distance 'd' between them is given by...

3. If $ \text {l, m and n} $ are the Direction cosines of a line and $ \text {a, b and c} $ are the Direction Ratios of the same line then...

4. Given parallel lines $ \vec{r} = \vec{a_1} + \lambda \vec{b} \ and \ \vec{r} = \vec{a_2} + \mu \vec{b} $, the shortest distance 'd' between them is given by ....

5. If $\frac{x-x_1}{l_1} = \frac{y-y_1}{m_1} = \frac{z-z_1}{n_1} $ and $\frac{x-x_2}{l_2} = \frac{y-y_2}{m_2} = \frac{z-z_2}{n_2} $ are the equations of two lines, then the acute angle between the two lines is given by $ \cos \theta = |l_1 l_2 + m_1 m_2 + n_1 n_2|$.