Recent questions in Three Dimensional Geometry

Find the equation of the plane passing through the point (1,4,-2) and parallel to the plane -2x+y-3z=7

asked Feb 5, 2013 by meena.p

0 answers

Show that the line $\bar{r}=(2\bar{i}-2\bar{j}+3\bar{k})+\lambda(\bar{i}-\bar{j}+4\bar{k})$ is parallel to the plane. $\bar{r}.(\bar{i}+5\bar{j}+\bar{k})=5$

asked Feb 5, 2013 by meena.p

0 answers

True or False: If the foot of perpendicular drawn from the origin to a plane is (5,-3,-2), then the equation of plane is $\overrightarrow{r}.(5\hat i-3\hat j-2\hat k)=38.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The equation of aline,which is parallel to $2\hat i\;-\hat j\;+\hat 3k$ and which passes through the point (5,-2,4) is $\Large \frac{x-5}{2}\;=\frac{y-2}{-1}\;=\frac{z-4}{3}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The vector equation of the line $\Large \frac{x-5}{3}\;=\frac{y+4}{7}\;=\frac{z-6}{2}$ is $\overrightarrow{r}=(5\hat i-4\hat j+6\hat k)+\lambda(3i\;+7j\;+2k).$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The line $\overrightarrow{r}=(2\hat i-3\hat j-\hat k)+\lambda(\hat i-2\hat j-2\hat k)$ lies in the plane $\overrightarrow{r}.(3\hat i-\hat j-\hat k)-2=0$

asked Jan 7, 2013 by sreemathi.v

0 answers

True or False: The angle between the planes $\overrightarrow{r}.(2\hat i-3\hat j+\hat k)=1$ and $\overrightarrow{r}.(\hat i- j)=4$ is $\cos^{-1}\Large \frac{-5}{\sqrt {58}}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The angle between the line $\overrightarrow{r}=(5\hat i-\hat j-\hat k)+\lambda(2\hat i-\hat j\;+\hat k)$ and the plane $\overrightarrow{r}.(3\hat i-4\hat j-\hat k)-5=0$ is $\sin^{-1}\large \frac{5}{2\sqrt 91}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The intercepts made by the plane $2x-3y+5z+4=0$ on the co-ordinate axis are $-2,\large\frac{4}{3},\frac{-4}{5}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The unit vector normal to the plane $x+2y+3z-6=0$ is $\large \frac{1}{\sqrt {14}}\hat i+\frac{2}{\sqrt {14}}\hat j+\frac{3}{\sqrt {14}}\hat k.$

asked Jan 6, 2013 by sreemathi.v

1 answer

The cartesian equation of the plane $\overrightarrow{r}.(\hat i\;+\hat j-\hat k)\;=2$ is ____________.

asked Jan 6, 2013 by sreemathi.v

1 answer

The vector equation of the line through the points $(3,4,-7)$ and $(1,-1,6)$ is ______________.

asked Jan 6, 2013 by sreemathi.v

1 answer

The vector equation of the line $\Large \frac{x-5}{3}\;\frac{y-4}{7}\;\frac{z-6}{2}$ is _______________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The direction cosines of the vector $(2\hat i+2\hat j-\hat k)$ are ___________.

asked Jan 4, 2013 by sreemathi.v

1 answer

A plane passes through the points $(2,0,0) (0,3,0)$ and $(0,0,4)$ .The equation of plane is__________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The plane 2x-3y+6z-11=0 makes an angle $\sin^{-1}(\alpha)$ with x-axis.The value of $\alpha$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

The locus represented by $xy+yz=0$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The area of the quadilateral $ABCD$ where $A(0,4,1),B(2,3,-1),C(4,5,0)$ and $D(2,6,2)$ is equal to

asked Jan 4, 2013 by sreemathi.v

1 answer

The reflection of the point $(\alpha,\beta,\gamma)$ in the xy-plane is

asked Jan 4, 2013 by sreemathi.v

1 answer

The sine of the angle between the straight line $\large \frac{x\;-2}{3}=\frac{y\;-3}{4}=\frac{z\;-4}{5}\;$ and the plane $2x-2y+z=5$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The distance of the plane $\overrightarrow{r}.\bigg(\frac{2}{7}\hat i+\frac{3}{7}\hat j-\frac{6}{7}\hat k\bigg)$ =1 from the origin is

asked Jan 4, 2013 by sreemathi.v

1 answer

If the directions cosines of a line are $k,k,k$ then

asked Jan 4, 2013 by sreemathi.v

1 answer

Distance of the point $(\alpha,\beta,\gamma)$ from y-axis is

asked Jan 4, 2013 by sreemathi.v

1 answer

If $l_1,m_1,n_1,l_2,m_2,n_2,l_3,m_3,n_3$ are direction cosines of three mutually perpendicular lines,prove that the line whose direction cosines are proportional to $l_1+l_2+l_3,m_1+m_2+m_3,n_1+n_2+n_3$ make equal angles with them.

asked Jan 4, 2013 by sreemathi.v

1 answer

Show that the straight lines whose direction cosines are given by $2l+2m-n=0\;and\;mn+nl+lm=0$ are at right angles.

asked Jan 4, 2013 by sreemathi.v

1 answer

$\overrightarrow{AB}=3 \hat i-\hat j+\hat k \;and\; \overrightarrow{CD}=-3\hat i+2 \hat j+4\hat k$ are two vectors. The position vectors of the points $A$ and $C$ are $6\hat i+7\hat j+4\hat k\;and\;-9\hat j+2\hat k,$ respectively.Find the position vector of a point $P$ on the line $AB$ and a point $Q$ on the line $CD$ such that $\overrightarrow{PQ}$ is perpendicular to $\overrightarrow{AB}\;and\;\overrightarrow{CD}$ both.

asked Jan 4, 2013 by sreemathi.v

1 answer

Show that the points $(\hat i-\hat j+3 \hat k)\; and\;3(\hat i+\hat j+\hat k)$ are equidistant from the plane $\overrightarrow{r}.(5 \hat i+2 \hat j-7 \hat k)+9=0$ and lies on opposite side of it.

asked Jan 4, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the intersection of the planes $\overrightarrow{r}.\quad(\hat i+3 \hat j)-6=0\; and\;\overrightarrow{r}.(3\hat i-\hat j-4 \hat k)=0,$ whose perpendicular distance from origin is unity.

asked Jan 4, 2013 by sreemathi.v

1 answer