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Questions asked by rvidyagovindarajan_1
Questions
870
questions
0
answers selected
The equation of the plane passing through the point $(3,2,0) $ and the line $\large\frac{x-3}{1}=\frac{y-6}{5}=\frac{z-4}{4}$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
medium
q25
asked
Dec 28, 2013
1
answer
The two lines whose equations are given by $x=ay+b,\:\:z=cy+d\:\:\:and\:\:\:x=a'y+b',\:\:z=c'y+d'$ are $\perp$ if
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
difficult
q24
asked
Dec 28, 2013
1
answer
The line $\overrightarrow r=(4\hat i+2\hat j+\alpha \hat k)+\lambda(\hat i+\hat j+2\hat k)$ lies on the plane $2x-4y+z=7$ if $\alpha=?$
jeemain
math
class12
ch11
3d-geometry
equations-of-planes
easy
q23
asked
Dec 28, 2013
1
answer
A line makes angle $\theta$ with $x\:\:and\:\:z\:\:axis.$ If it makes angle $\beta$ with $y\; axis$, where $sin^2 \beta=3sin^2\theta$, then $ cos^2\theta=?$
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
medium
q22
asked
Dec 28, 2013
1
answer
If the lines $x=1+s,\:y=3-\lambda s,\:z=1+\lambda s\:\:and\:\:x=\large\frac{t}{2}$, $y=1+t,\:z=2-t$ where $s\:\:and\:\:t$ are parameters, are $coplanar$, then $\lambda=?$
jeemain
math
class12
ch11
3d-geometry
coplanar-lines
easy
q21
asked
Dec 28, 2013
1
answer
The distance of the line $\overrightarrow r=2\hat i-2\hat j+3\hat k+\lambda(\hat i-\hat j+4\hat k)$ from the plane $x+5y+z=5$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
difficult
q20
asked
Dec 28, 2013
1
answer
$L$ is line of intersection of the planes $2x+3y+z=1\:\:and\:\:x+3y+2z=2$ and $\alpha$ is the angle made by the line $L$ with positive $x-axis$ then $cos\alpha=?$
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
difficult
q19
asked
Dec 28, 2013
1
answer
The line through the points $(5,1,a)\:\:and\:\:(3,b,1)$ crosses $yz$ plane at the point $(0,\large\frac{17}{2},-\frac{13}{2})$, then $(a,b)=?$
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
q18
medium
asked
Dec 27, 2013
1
answer
If $P(3,2,6)$ is a point and $Q$ is a point on the line $\overrightarrow r=(\hat i-\hat j+2\hat k)+\lambda(-3\hat i+\hat j+5\hat k),$ then the value of $\lambda$ for which $\overrightarrow {PQ}$ is parallel to the plane $x-4y+3z=1$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-lines-and-planes
medium
q17
asked
Dec 27, 2013
1
answer
If a line $\overline {AB}$ makes angle $45^{\circ}$ with positive $x-axis$ and $120^{\circ}$ with positive $y-axis$, then the angle $\theta$ made by the line with positive $z-axis$ is ?
jeemain
math
class12
ch11
3d-geometry
direction-cosines
easy
q16
asked
Dec 27, 2013
1
answer
If the distance of the point $P(1,-2,1)$ from the plane $x+2y-2z=a$, where $a>0,$ is $5$, then the foot of the $\perp$ from $P$ to this plane is ?
jeemain
math
class12
ch11
3d-geometry
intersection-between-a-plane-and-a-line
difficult
q15
asked
Dec 27, 2013
1
answer
The length of the perpendicular drawn from the point $(3,-1,11) $ on the line $\large\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is?
jeemain
math
class12
ch11
3d-geometry
equation-of-a-line
medium
q14
asked
Dec 27, 2013
1
answer
The distance of the point $(1,-5,9) $ from the plane $x-y+z=5$ measured along the line $x=y=z$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-between-a-plane-and-a-line
medium
q13
asked
Dec 26, 2013
1
answer
If the lines $\overrightarrow r=(\hat i-\hat j+\hat k)+\lambda(2\hat i+3\hat j+4\hat k)\:\:and\:\:\overrightarrow r=(3\hat i+k\hat j)+\mu(\hat i+2\hat j+\hat k)$ intersect then $k=?$
jeemain
math
class12
ch11
3d-geometry
intersection-between-lines
easy
q12
asked
Dec 26, 2013
1
answer
The equation of the plane which is parallel to the plane $x-2y+2z-5=0$ and which is at a unit distance from origin is ?
jeemain
math
class12
ch11
3d-geometry
equation-of-a-plane
medium
q11
asked
Dec 26, 2013
1
answer
The equation of the plane passing through the line of intersection of the planes $x+2y+3z-2=0\:\:and\:\:x-y+z-3=0$ and which is at a distance of $\large\frac{2}{\sqrt 3}$ units from $(3,1,-1)$. is ?
jeemain
math
class12
q14
medium
q10
asked
Dec 26, 2013
1
answer
If $P$ is the point of intersection of the line joining the points $Q(2,3,5)\:\:and\:\:R(1,-1,4)$ with the plane $5x-4y-z-1=0$. If $S$ is foot of $\perp$ drawn from the point $T(2,1,4)$ to the line $QR$, then the length of segment $\overrightarrow {PS}$ = ?
jeemain
math
class12
ch11
3d-geometry
intersection-of-a-line-and-a-plane
difficult
q9
asked
Dec 25, 2013
1
answer
If the lines $\large\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\large\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are co planar then the plane containing these two lines is?,
jeemain
math
class12
ch11
3d-geometry
coplanar-lines
difficult
q8
asked
Dec 25, 2013
1
answer
The intercepts cut off by the plane $\overrightarrow r.(2\hat i+\hat j-\hat k)=5$ with the axes are ?
jeemain
math
class12
ch11
3d-geometry
equation-of-a-plane
easy
q7
asked
Dec 24, 2013
1
answer
A line with positive direction cosines passes through the point $ P(2,-1,2)$ and makes equal angle with coordinate axes. The line meets the plane $2x+y+z=9$ at the point $Q$. The length of the segment $PQ$=?
jeemain
math
class12
ch11
3d-geometry
intersection-between-a-line-and-a-plane
difficult
q6
asked
Dec 23, 2013
1
answer
If the line $\large\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z-2}{2}$ lie in the plane $x+3y-\alpha z+\beta=0, \;\;then\:\:(\alpha,\beta)=?$
jeemain
math
class12
ch11
3d-geometry
intersection-between-a-line-and-a-plane
medium
q5
asked
Dec 23, 2013
1
answer
The distance of the plane $2x-3y+6z+14=0$ from origin is ?
jeemain
math
class12
ch11
3d-geometry
equation-of-a-plane
easy
q4
asked
Dec 22, 2013
1
answer
The line $\overrightarrow r=\hat i+2\hat j-\hat k+\lambda(2\hat i-\hat k)$ is $\perp$ to which axis?
jeemain
math
class12
ch11
3d-geometry
equations-of-lines
easy
q3
asked
Dec 18, 2013
1
answer
The angle between the line $\overrightarrow r=(2\hat i-\hat j+3\hat k)+\lambda(3\hat i-\hat j+2\hat k)\:\:and\:\:the\:\:plane\:\:\overrightarrow r.(\hat i+\hat j+\hat k)=3$ is ?
jeemain
math
class12
ch11
3d-geometry
intersection-between-a-line-and-a-plane
easy
q2
asked
Dec 18, 2013
1
answer
The distance between the parallel planes $2x+3y+4z=5\:\:and\:\:4x+6y+8z=12$ is ?
jeemain
math
class12
ch11
3d-geometry
equations-of-a-plane
easy
q1
asked
Dec 17, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b$ are two non zero and non collinear vectors, then $[\overrightarrow a\:\overrightarrow b\:\hat i]\hat i+[\overrightarrow a\:\overrightarrow b\:\hat j]\hat j+[\overrightarrow a\:\overrightarrow b\:\hat k]\hat k=?$
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q100
asked
Dec 17, 2013
1
answer
A parallelogram has adjacent sides $\overrightarrow a=3\overrightarrow p-\overrightarrow q\:\;and\:\:\overrightarrow b=\overrightarrow p+3\overrightarrow q$ where $ |\overrightarrow p|=|\overrightarrow q|=2$, and the angle between $\overrightarrow p\:\:and\:\:\overrightarrow q$ is $\large\frac{\pi}{3}$. The length of its diagonals are?
jeemain
class12
ch10
vector-algebra
medium
addition-of-vectors
q99
asked
Dec 13, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j+p\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j+\hat k$, then $|\overrightarrow a+\overrightarrow b|=|\overrightarrow a|+|\overrightarrow b|$ holds for ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q98
asked
Dec 10, 2013
1
answer
If $\overrightarrow {\alpha}=(x+4y)\overrightarrow a+(2x+y+1)\overrightarrow b\:\:and\:\:\overrightarrow {\beta}=(y-2x+2)\overrightarrow a+(2x-3y-1)\overrightarrow b$ where $\overrightarrow a\:\:\overrightarrow b$ are non zero non collinear and if $3\overrightarrow {\alpha}=2\overrightarrow {\beta}$, then $(x,y)=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q97
asked
Dec 10, 2013
1
answer
If a person standing at the point $(1,2) $ walks $5$ units towards east, then $3$ units towards north and $\sqrt 2$ units along the direction of $\hat i+\hat j$ and then walks $\sqrt 2 $ unit along the direction $\perp$ to this vector towards the starting point. What is the displacement of the person from origin?
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q96
asked
Dec 9, 2013
1
answer
If $\overrightarrow a+2\overrightarrow b+3\overrightarrow c=\overrightarrow 0$, then $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q95
asked
Dec 8, 2013
1
answer
If $\overrightarrow a=2p\hat i+\hat j$ is rotated about an angle of $\theta$ in anti clock wise direction and becomes $(p+1)\hat i+\hat j$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q94
asked
Dec 8, 2013
1
answer
If $\overrightarrow {AB}=3\hat i-2\hat j+2\hat k$ and $\overrightarrow {BC}=-\hat i-2\hat k$ are adjacent sides of a parallelogram, then the angle between the diagonals is ?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q93
asked
Dec 8, 2013
1
answer
If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are unit vectors that are inclined at angle $2\theta$ where $0\leq \theta \leq \pi$ and $|\overrightarrow a-\overrightarrow b| < 1$ then $ \theta$ lies in the interval....
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q92
asked
Dec 8, 2013
1
answer
If $\overrightarrow b\:\:is\:\: \perp\:\:to \:\:\overrightarrow a+\overrightarrow b\:\:and\:\:\overrightarrow a\:\:is\:\:\perp \:\:to\:\:2\overrightarrow b+\overrightarrow a$ then $|\overrightarrow a|=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q91
asked
Dec 8, 2013
1
answer
If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors such that $\overrightarrow a+2\overrightarrow b\:\:and\:\:5\overrightarrow a-4\overrightarrow b$ are $\perp$ to each other, then the angle between $\overrightarrow a\:\:and\:\:\overrightarrow b$ is?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q90
asked
Dec 8, 2013
1
answer
If $\overrightarrow a\:and\:\overrightarrow b$ are two non collinear unit vectors and $\overrightarrow u=\overrightarrow a-(\overrightarrow a.\overrightarrow b)\overrightarrow b\:\:and\:\:\overrightarrow v=\overrightarrow a\times\overrightarrow b$, then $|\overrightarrow v|=?$
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q89
asked
Dec 8, 2013
1
answer
If $\overrightarrow v=2\hat i+\hat j-\hat k, \:\:and\:\:\overrightarrow w=\hat i+3\hat k\:\:and\:\:\overrightarrow u$ is a unit vector, then the maximum value of $[\overrightarrow u\:\overrightarrow v\:\overrightarrow w]=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q88
asked
Dec 8, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are unit vectors, then the maximum value of $|\overrightarrow a-\overrightarrow b|^2+|\overrightarrow b-\overrightarrow c|^2+|\overrightarrow c-\overrightarrow a|^2$ is ?
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q87
asked
Dec 7, 2013
1
answer
If $|\overrightarrow a|=|\overrightarrow c|=1, \:|\overrightarrow b|=4,\:\overrightarrow a\times\overrightarrow b=2\overrightarrow a\times\overrightarrow c\:and\:$ if the angle between $\overrightarrow b\:and\:\:\overrightarrow c$ is $cos^{-1}\large\frac{1}{4}$ then $\overrightarrow b-2\overrightarrow c=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q86
asked
Dec 7, 2013
1
answer
The number of vectors $\overrightarrow b$ of unit length which are $\perp$ to $\overrightarrow a=\hat i+2\hat j\:\:and\:\:\overrightarrow c=\hat j+2\hat k$ is?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q85
asked
Dec 7, 2013
1
answer
If $\overrightarrow a\:\:and\:\:\overrightarrow b$ are two unit vectors, then $\overrightarrow a\times\overrightarrow b$ is also a unit vector if ?
jeemain
math
class12
ch10
vector-algebra
easy
vector-product
q84
asked
Dec 7, 2013
1
answer
If $\overrightarrow a\times\overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a$ and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ are $\perp$ then $\overrightarrow a,\:\overrightarrow b\:\overrightarrow c$ are .....
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q83
asked
Dec 7, 2013
1
answer
If $\overrightarrow a$ is any vector such that $\overrightarrow a\times \hat i+2\overrightarrow a-5\hat k=\overrightarrow 0$, then $\overrightarrow a=?$
jeemain
math
class12
ch10
vector-algebra
medium
addition-of-vectors
q82
asked
Dec 6, 2013
1
answer
If $\overrightarrow d=x(\overrightarrow a \times\overrightarrow b)+y(\overrightarrow b\times\overrightarrow c)+z(\overrightarrow c\times\overrightarrow a)$ and $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=\large\frac{1}{8}$, then $x+y+z=?$
jeemain
math
class12
ch10
vector-algebra
difficult
addition-of-vectors
q81
asked
Dec 6, 2013
1
answer
If $\overrightarrow a=p\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow b=\sqrt q\hat i+5\hat k$ are two vectors of same magnitude, then no. of values of $(p,q)$ are?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q80
asked
Dec 6, 2013
1
answer
If $\overrightarrow a=\hat i+\hat j-\hat k,\:\overrightarrow b=-\hat i+2\hat j+\hat k\:\:and\:\:\overrightarrow c=-\hat i+2\hat j-\hat k$, then a unit vector $\perp$ to $\overrightarrow a+\overrightarrow b$ and $\overrightarrow b+\overrightarrow c$ is ?
jeemain
math
class12
ch10
vector-algebra
easy
addition-of-vectors
q79
asked
Dec 6, 2013
1
answer
A man walks 4 mtrs. towards west and then walks 3 mtrs in the direction of $\large\frac{\pi}{6}\:$ radians east of north. What is the displacement of the man from the starting point?
jeemain
math
class12
ch10
vector-algebra
difficult
vector-product
q78
asked
Dec 5, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three unit vectors such that $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c=0$ and the angle between $\overrightarrow b\:\:and\:\:\overrightarrow c $ is $\large\frac{\pi}{6}$, then $\overrightarrow b\times\overrightarrow c=?$
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q77
asked
Dec 5, 2013
1
answer
If $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three vectors such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow b\times\overrightarrow c=\overrightarrow a$, then the magnitude of $\overrightarrow b$ is?
jeemain
math
class12
ch10
vector-algebra
medium
vector-product
q76
asked
Dec 5, 2013
1
answer
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