Recent questions tagged p498

Find the equation of the plane passing through the line of intersection of the planes $\overrightarrow r. (\hat i + \hat j + \hat k)=1$ and $ \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0$ and parallel to $x$ - axis.

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\hat{r}. (\hat{i}+\hat{j}+\hat{k}) = 2$.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If the points $( 1, 1 , p)$ and $(– 3 , 0, 1)$ be equidistant from the plane $\hat{r} . (3\hat{i} +4\hat{j} -12\hat{k} +13) = 0$ then find the value of $p$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane passing through the point $( -1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.

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

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

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Find the equation of the plane passing through the line of intersection of the planes \(\overrightarrow r. (\hat i + \hat j + \hat k)=1\) and \( \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0\) and parallel to \(x\) - axis.

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\hat{r}. (\hat{i}+\hat{j}+\hat{k}) = 2$.

If the points $( 1, 1 , p)$ and $(– 3 , 0, 1)$ be equidistant from the plane $\hat{r} . (3\hat{i} +4\hat{j} -12\hat{k} +13) = 0$ then find the value of $p$.

Find the equation of the plane passing through the point $( -1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.

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

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

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

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 $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$

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

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 $k$.

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 $CD$.

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

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