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Questions >> CBSE XII >> Math >> Three Dimensional Geometry

Find the shortest distance between lines $\hat{r} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda ( \hat{i} - 2\hat{j} + 2\hat{k} )$ and $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the vector equation of the line passing through $(1, 2, 3)$ and perpendicular to the plane $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$ .

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the coordinates of the points $A, B, C, D$ be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 9, 2) respectively, then find the angle between the lines $AB$ and $CD$ .

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of a line parallel to x-axis and passing through the origin.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If $l_1, m_1, n_1$ and $l _2, m_2, n_2$ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are $m_1n_2-m_2n_1$ , $n_1l_2-n_2l_1$ , $l_1m_2-l_2m_1$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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