Recent questions and answers in Three Dimensional Geometry

Find the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3)

answered Nov 10, 2018 by gargtanu21

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Coloured balls are distributed in three bags as shown in the table below, a bag is selected at random and then two balls are randomly drawn from the selected bag. They happen to be black and red. what is the probability that they came from bag 1 ?

answered Nov 7, 2018 by classicshameer10

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The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle $\alpha$.Prove that the equation of the plane in its new position is $ax+by\pm \bigg(\sqrt {a^2+b^2}\tan \alpha\bigg)z=0$.

answered Feb 4, 2018 by sanjamdeep30

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Find the values of P so that the lines $ \Large\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $ \Large\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles.

answered Jan 23, 2018 by adarsh06032000

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Find the equation of the plane passing through the point (1,6,3) and perpendicular to the plane 2x+3y-z = 7

answered May 22, 2017 by vikkyravi0106

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A variable plane is at constant distance p from the origin and meet the axes in A, B & C. Show that the locus of the centroid of the tetrahedron $\bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{16}{p^2}$

answered Feb 4, 2017 by loserlady2lol

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A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B & C. Show that the locus of the centroid of the $ \bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$

answered Feb 4, 2017 by loserlady2lol

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Find the equation of the plane passing through the points (1,-1,2) and (2,-2,2) and perpendicular to the plane 6x-2y+2z = 9.

answered Sep 3, 2015 by meena.p

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If the lines $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\lambda(3\hat i+2k\hat j-2\hat k)$ and $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\mu(k\hat i+\hat j+5\hat k)$ are $\perp$ to one another then find the equation of the plane containing them.

answered Feb 4, 2014 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.

answered Feb 3, 2014 by rvidyagovindarajan_1

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

answered Feb 3, 2014 by rvidyagovindarajan_1

1 answer

find the radius of cicular section of sphere x^2+y^2+z^2=49 by the plane 2x+3y-z-4(14)^1/2

asked Dec 28, 2013 by ankitclusters_1

0 answers

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

answered Nov 7, 2013 by pady_1

1 answer

Are the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) collinear?

answered Jul 20, 2013 by balaji.thirumalai

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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 $\overrightarrow{r}.(5\hat i-3\hat j-2\hat k)=38.$

answered Jun 15, 2013 by meena.p

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 $\Large \frac{x-5}{2}\;=\frac{y-2}{-1}\;=\frac{z-4}{3}.$

answered Jun 13, 2013 by meena.p

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\[\overrightarrow{r}=(5\hat i-4\hat j+6\hat k)+\lambda(3i\;+7j\;+2k).\]

answered Jun 13, 2013 by meena.p

1 answer

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 $\cos^{-1}\Large \frac{-5}{\sqrt {58}}.$

answered Jun 13, 2013 by meena.p

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 $\sin^{-1}\large \frac{5}{2\sqrt 91}.$

answered Jun 13, 2013 by meena.p

1 answer

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

answered Jun 13, 2013 by meena.p

1 answer

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

answered Jun 13, 2013 by meena.p

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

answered Jun 13, 2013 by meena.p

1 answer