Recent questions tagged 3d-geometry

If $A,B,C$ are three points on $x\:axis,\:y\:axis\:and\:z\:axis$ respectively which are at the distances $a,b,c$ from origin respectively and $P$ is a point which is equidistant from $A,B,C,O$ then the coordinates of $P$ is?

asked Jan 21, 2014 by rvidyagovindarajan_1

1 answer

If $A(4,7,8),\:B(2,3,4),\:C(2,5,7)$ are vertices of a triangle then the length of internal bisector of angle $A$ is ?

asked Jan 12, 2014 by rvidyagovindarajan_1

1 answer

Find the angle between any two diagonals of a cube.

asked Jan 12, 2014 by rvidyagovindarajan_1

1 answer

The cosine of angle between the medians drawn from vertices of isosceles rt. angled triangle is?

asked Jan 12, 2014 by rvidyagovindarajan_1

1 answer

If from a point $P(a,b,c)$ perpendiculars $PA,\:PB,\:$ are drawn on $yz\:\:and\:\:zx$ planes. then the equation of the plane $OAB$ is ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

If the vertices of a triangle are $A(1,4,2),\:B(-2,1,2)\:C(2,-3,4)$ then the angle $B$ = ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

The projection of a line segment on $x,y,z$ axes are $12,\:4,\:3$ respectively, then the length of the line segment is ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

The locus of a point $(x,y,z)$ for which $z=k$ is a ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

The points $(5,0,2),\:(2,-6,0),\:(4,-9,6)\:and\:(7,-3,8)$ represent vertices of a ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

A line segment of length $21$ has $d.r.=(2,-3,6)$ and makes obtuse angle with $x\:axis$, then the components of the line segment (vector) are?

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

If $P(2,3,4)\;and\:Q(1,b,1)$ are two points and $O$ is origin such that $OP$ is $\perp$ to $OQ$, then $b=?$

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

The point which divides the line joining the points $(2,4,5)\:\:and\:\:(3,5,-4)$ in the ratio $2:3$ externaly lies on the plane?

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

If the plane $x-2y+3z=0$ is rotated through a right angle about its line of intersection with the plane $2x+3y-4z-5=0$, then the eqn. of the plane in its new position is ?

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

The angle between the line formed by $3x-7y-5z=1$ and $8x-11y+2z=0$ and the line formed by $5x-13y+3z+2=0$ and $8x-11y+2z=0$

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

Equation of the line through the point $(2,-1,-1)$, which is parallel to the plane $4x+y+z+2=0$ ans is $\perp$ to the line $x=\large\frac{y}{-2}=$$z-5$ is ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

The equation of projection of the line $\large\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{3}$ on the plane $x+y+z=1$ is given by ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

The direction cosine of a line which is $\perp$ to two perpendicular lines whose direction cosines are $(l_1,m_1,n_1)\:\:and\:\:(l_2,m_2,n_2)$ is ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane that meets the coordinate axes at the points $A,B,C$ respectively and the centroid of the $\Delta\:ABC$ is $(2,1,5)$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane which makes double the intercepts of the plane $3x+6y-z+12=0$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

A line makes angle $\theta$ with both $x\:axis$ and $z\:axis$. If it makes angle $\alpha$ with $y\:axis$ and $\sin^2\alpha=2 \sin^2\theta$ then $\cot^2\theta=?$

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

A tetrahedron has vertices $O(0,0,0),\:A(1,2,1)\:B(2,1,3)\:C(-1,1,2)$. The angle between the faces $OAB$ and $ABC$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The value of $k$ for which the line $\overrightarrow r=(4\hat i+2\hat j-\hat k)+\lambda(\hat i-k\hat j+2\hat k)$ lies on the plane $2x-4y+z=3$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The value of $k$ for which the line $\large\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ to lie on the plane $2x-4y+3z=6$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

A line with direction ratio $(2,1,2)$ meets the lines $x=y+a=z\:\;and\:\:x+a=2y=2z$. The coordinates of the points of intersections are ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

A variable plane is at a distance $k$ from origin and meets the coordinate axes at the points $A,B,C$ respectively. then the locus of centroid of the $\Delta\:ABC$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane passing through the point $(1,1,1)$ and having direction ratios $b,c,a$ $(a < b < c)$, where $a,b,c$ are prime factors of $2001$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $P(0,1,0)\:and\:Q(0,0,1)$ are two points in space, then the projection of $PQ$ on the plane $x+y+z=3$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

Distance of a point $P(\overrightarrow c)$ from the the line $\overrightarrow r=\overrightarrow a+\lambda \overrightarrow b$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

A vector $\overrightarrow a$ is parallel to the line of intersection of planes $P_1$ containing vectors $\hat i,\:\hat i+\hat j$ and $P_2$ conataining vectors $\hat i-\hat j,\:\hat i+\hat k$. Then the angle between $\overrightarrow a$ and $\hat i-2\hat j+2\hat k$ is?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

The vectors $\overrightarrow a,\overrightarrow b,\overrightarrow c\:\overrightarrow d$ be are such that $(\overrightarrow a\times\overrightarrow b)\times (\overrightarrow c\times\overrightarrow d)=0$ and $P_1,\:P_2$ are two planes containing the pair of vectors $\overrightarrow a,\overrightarrow b$ and $\overrightarrow c,\overrightarrow d$ respectively, then the angle between the planes is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

A line passes through the points with position vectors are $\hat i+\hat j-2\hat k$ and $\hat i-3\hat j+\hat k$. The position vector of a point on the line which is at a unit distance from the first point is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are position vectors of three non collinear points $A,B,C$ respectively, then the shortest distance of $A$ from $BC$ is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

The distance of the point $(1,1,1) $ from the plane passing through the points $(2,1,1),\:(1,2,1)\:and\:(1,1,2)$ is ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

The line joining the points $6\overrightarrow a-4\overrightarrow b-5\overrightarrow c$ and $-4\overrightarrow c$ and the line joining the points $-\overrightarrow a-2\overrightarrow b-3\overrightarrow c$ and $\overrightarrow a+2\overrightarrow b-5\overrightarrow c$ Intersects at the point ?

asked Jan 5, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane having intercepts of $3$ and $4$ with $x$ and $z$ axes respectively and parallel to $y$ axis is ?

asked Jan 4, 2014 by rvidyagovindarajan_1

1 answer

If the lines $x=1+s,\:y=-3-\lambda s,\:z=1+\lambda s$ and $x=t/2,\:y=1+t,\:z=2-t$ with parameters $s\:and\:t$ respectively, are coplanar, then $\lambda=?$

asked Jan 4, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane containing the lines $\overrightarrow r=\overrightarrow a_1+\lambda\overrightarrow b\:\:and\:\:\overrightarrow r=\overrightarrow a_2+\mu\overrightarrow b$ is ?

asked Jan 4, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane that contains the line $\overrightarrow r=2\hat i+\lambda(\hat j-\hat k)$ and $\perp$ to the plane $\overrightarrow r.(\hat i+\hat k)=3$ is ?

asked Jan 4, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane through the point $(1,2,-1)$ and $\perp$ to the line of intersection of the planes $\overrightarrow r.(3\hat i-\hat j+\hat k)=1$ and $\overrightarrow r.(\hat i+4\hat j-2\hat k)=2$ is?

asked Jan 4, 2014 by rvidyagovindarajan_1

1 answer