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Recent questions tagged sec-b

Choose the correct answer in the distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If O be the origin and the coordinates of P be $(1, 2, – 3)$, then find the equation of the plane passing through P and perpendicular to OP.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane which contains the line of intersection of the planes $\hat{r} . (\hat{i} + 2\hat{j} +3\hat{k}) - 4 = 0$ and $\hat{r} . (2\hat{i} + \hat{j} - \hat{k}) + 5 = 0$ and which is perpendicular to the plane $\hat{r} . (5\hat{i} + 3\hat{j} -6\hat{k}) +8 = 0$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through $(3, – 4, – 5)$ and $(2, – 3, 1)$ crosses the plane $2x + y + z = 7.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through $(5, 1, 6)$ and $(3, 4, 1)$ crosses the YZ-plane.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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

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

If $$\overrightarrow{a} ,\overrightarrow{b} , \overrightarrow{c}$$ are mutually perpendicular vectors of equal magnitudes, show that the vector $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}$$ is equally inclined to $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c} $$.

asked Nov 2, 2012 by balaji.thirumalai

0 answers

Show that the points A (1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Nov 2, 2012 by balaji.thirumalai

0 answers

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