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Recent questions and answers in 3-D Geometry
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3-D 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?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q99
answered
Jan 23, 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 ?
jeemain
math
class11
ch12
3d-geometry
easy
distance-between-two-points
q98
mock
answered
Jan 12, 2014
by
rvidyagovindarajan_1
1
answer
Find the angle between any two diagonals of a cube.
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q97
answered
Jan 12, 2014
by
rvidyagovindarajan_1
1
answer
The cosine of angle between the medians drawn from vertices of isosceles rt. angled triangle is?
jeemain
math
class12
ch12
3d-geometry
direction cosines
easy
q96
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q95
answered
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 $B$ = ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q94
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q93
answered
Jan 11, 2014
by
rvidyagovindarajan_1
1
answer
The locus of a point $(x,y,z)$ for which $z=k$ is a ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q92
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q91
answered
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?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q90
answered
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 $b=?$
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q89
answered
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?
jeemain
math
class11
ch12
3d-geometry
section formula
easy
q88
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q87
answered
Jan 10, 2014
by
rvidyagovindarajan_1
1
answer
The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q86
answered
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 $8x-11y+2z=0$
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q85
answered
Jan 9, 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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
difficult
q83
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q84
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
direction cosines
easy
q82
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q81
answered
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 ?
jeemain
math
class12
3d-geometry
easy
equations-of-planes
q80
ch11
answered
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 $\cot^2\theta=?$
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
medium
q79
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q78
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q77
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q76
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q75
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q74
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q73
answered
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 ?
jeemain
math
class11
ch11
3d-geometry
coordinate-axes-and-planes
easy
q72
answered
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 ?
jeemain
math
class11
ch11
3d-geometry
distance-between-two-points
easy
q71
answered
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?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q70
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q69
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
easy
q68
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
medium
q67
answered
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 ?
jeemain
math
class11
ch12
3d-geometry
distance-between-two-points
medium
q66
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q65
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
easy
q64
answered
Jan 5, 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 $\lambda=?$
jeemain
math
class12
ch11
3d-geometry
coplanar-lines
difficult
q63
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q62
answered
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 ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q61
answered
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?
jeemain
math
class12
ch11
3d-geometry
medium
intersection-of-lines-and-planes
q60
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
If the position vector of the points $A\:and\:B$ are $\hat i-\hat j+3\hat k$ and $3\hat i+3\hat j+3\hat k$ and the equation of a plane is $\overrightarrow r.(5\hat i+2\hat j-7\hat k)+9=0$, then the points $A\:and\:B$ are?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
easy
q59
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane through origin and the line of intersection of the planes $\overrightarrow r.\overrightarrow a=\lambda\:\:and\:\:\overrightarrow r.\overrightarrow b=\mu$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
easy
q58
answered
Jan 4, 2014
by
rvidyagovindarajan_1
1
answer
If $O$ is origin, $OP=3$ with $d.r.=(-1,2,-2)$ then the coordinate of $P$ is ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
easy
q57
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
If $P(x,y,z)$ is a point on the line segment joining $Q(2,2,4)\:\:and\:\:R(3,5,6)$ such that the projections of $\overrightarrow {OP}$ on the coordinate axes are $\large\frac{13}{5},\frac{19}{5},\frac{26}{5}$ respectively, then $P$ divides $QR$ in the ratio ?
jeemain
math
class11
ch12
3d-geometry
coordinate-axes-and-planes
medium
q56
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
If $P$ is a point in space such that $OP=12$ and $\overrightarrow {OP} $ is inclined with angle $45^{\circ} $ with $OX$ and $60^{\circ}$ with $OY$ then the coordinates of $P$ is ?
jeemain
math
class11
ch12
3d-geometry
coordinates-of-a-point-in-space
easy
q55
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
If $P(3,2,-4),\:Q(5,4,-6)\:and\:R(9,8,-10)$ are collinear,then $R$ divides $PQ$ in ratio?
jeemain
math
class11
ch12
3d-geometry
section-formula
easy
q54
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The length of $\perp$ from origin to the plane passing through the point $\overrightarrow a$ and containing the line $\overrightarrow r=\overrightarrow b+\lambda \overrightarrow c$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q53
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The equation of the plane through the line of intersection of the planes $ax+by+cz=d=0$ and $a'x+b'y+c'z+d'=0$ and parallel to the line $y=0,z=0$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q52
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The line through the point $\hat i+3\hat j+2\hat k$ and $\perp$ to the lines $\overrightarrow r=(\hat i+2\hat j-\hat k)+\lambda(2\hat i+\hat j+\hat k)$ and $\overrightarrow r=(2\hat i+6\hat j+\hat k)+\mu (\hat i+2\hat j+3\hat k)$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q51
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
The distance of the point $(-1,2,6)$ from the line through the point $(2,3,-4)$ along the vector $6\hat i+3\hat j-4\hat k$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q50
answered
Jan 3, 2014
by
rvidyagovindarajan_1
1
answer
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