Processing math: 1%

CBSE Questions for Class 12 Commerce Maths Three Dimensional Geometry Quiz 8 - MCQExams.com

ABC is a triangle where A=(2,3,5),B=(1,2,2) and C(λ,5,μ) if the median through A is equally inclined to the positive axis then λ+μ is 
  • 7
  • 6
  • 15
  • 9
Projection of a vector on 3 coordinate axes are 6, - 3, 2 respectively. Then DC's of vector are-
  • 6, - 3, 2
  • \dfrac{6}{5},\dfrac{{ - 3}}{5},\dfrac{2}{5}
  • \dfrac{-6}{7},\dfrac{{ - 3}}{2},\dfrac{2}{7}
  • \dfrac{  6}{7},\dfrac{{ - 3}}{7},\dfrac{2}{7}
If the foot of the perpendicular from (0,0,0) to a plane is P(1,2,2). Then, the equation of the plane is
  • -x+2y+8z-9=0
  • x+2y+2z-9=0
  • x+y+z-5=0
  • x+2y-3z+3=0
P\left(1,1,1\right) and Q\left(\lambda,\lambda,\lambda\right) are two points in the space such that PQ=\sqrt{27}, the value of \lambda can be 
  • -4
  • -2
  • 2
  • 0
A(2,3,7),B(-1,3,2) and C(q,5,r) are the vertices of \Delta ABC. If the median through A is equally inclined to the coordinate axes then the coordinates of the vertex C is
  • (7,5,14)
  • (7,5,12)
  • (7,5,10)
  • (7,5,16)
If the points \bar a + \bar b,\bar a - \bar b,\bar a + k\bar b are collinear, then  
  • k has only one real value
  • k has two real value
  • k has no real values
  • k has infinite number of real values
A line AB in three-dimensional space males angles {45}^{o} and {120}^{o} with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle \theta with the positive z-axis, then \theta equal
  • {45}^{o}
  • {60}^{o}
  • {75}^{o}
  • {30}^{o}
If the points (\alpha, - 1), (2, 1) and (4, 5) are collinear, then find \alpha by vector method.
  • 4
  • 1
  • 8
  • None of these
The Cartesian equation of line 6x - 2 = 3y + 1 = 2z - 2 is given by

  • \dfrac{{3x - 1}}{3} = \dfrac{{3y + 1}}{6} = \dfrac{{z - 1}}{3}
  • \dfrac{{3x + 1}}{3} = \dfrac{{3y - 1}}{6} = \dfrac{{z - 1}}{3}
  • \dfrac{{3x - 1}}{3} = \dfrac{{3y - 1}}{6} = \dfrac{{z - 1}}{3}
  • \dfrac{{3x - 1}}{6} = \dfrac{{3y - 1}}{3} = \dfrac{{z - 1}}{3}
The direction ratios of the joining A(1,\,2,\ 1) and (2,\ 1,\ 2) are
  • 3,\ 3,\ 3
  • -1,\ 1,\ -1
  • 3,\ 1,\ 3
  • \dfrac{1}{\sqrt{3}},\ \dfrac{1}{\sqrt{3}},\ \dfrac{1}{\sqrt{3}}
The direction ratios of AB are - 2, 2, 1 . If coordinates of A are ( 4,1,5 ) and l( A B ) = 6 , then coordinates of B ?
  • ( 0,5 , - 7 )
  • ( 8 , - 3,3 )
  • ( 0,7,5 )
  • ( 8,3,3 )
If the lines {L}_{1}\ and {L}_{2} are given by \bar { r } =\left( \bar { i } +2\bar { j } -\bar { k }  \right) +t\left( \bar { 2i } -3\bar { j } +\bar { k }  \right) \ and\bar { r } =\left( \bar { i } +\bar { j } +\bar { k }  \right) +s\left( 2\bar { i } +\bar { j } -\bar { k }  \right), then 
  • {L}_{1}\ and {L}_{2} are perpendicular
  • {L}_{1}\ and {L}_{2} are parallel
  • \left ({L}_{1},{L}_{2}\right)={45}^{o}
  • \left ({L}_{1},{L}_{2}\right)={60}^{o}
The vector equation of line passing through the point (-1,-1,2) and parallel to the line 2x-2=3y+1=6z-2
  • (-\hat { i } -\hat { j } +2\hat { k } )+\lambda (3\hat { i } +2\hat { j } +\hat { k } )
  • (-\hat { i } -\hat { j } +2\hat { k } )+\lambda (2\hat { i } +3\hat { j } +6\hat { k } )
  • (-\hat { i } -\hat { j } +2\hat { k } )+\lambda (\hat { i } +2\hat { j } +3\hat { k } )
  • (-\hat { i } -\hat { j } +2\hat { k } )+\lambda (2\hat { i } +3\hat { j } +\hat { k } )
If \bar {a}, \bar {b} and \bar {c} are non-zero non collinear vectors and \theta(\neq 0 , \pi) is the angle between \bar {b} and \bar {c} if (\bar {a}\times \bar {b}) \times \bar {c}=\dfrac {1}{2} |\bar {b}|\bar {c}|\bar {a}. then \sin \theta =
  • \sqrt{\dfrac{2}{3}}
  • \dfrac{\sqrt{3}}{2}
  • \dfrac{4\sqrt{2}}{3}
  • \dfrac{2\sqrt{2}}{3}
If A=(1,2,-1), B=(2,0,3), C=(3,-1,2) then the angle between \overline { AB } and \overline { AC } is
  • {0}^{o}
  • {90}^{o}
  • \cos ^{ -1 }{ \left( \cfrac { 20 }{ \sqrt { 21 } \sqrt { 22 } } \right) }
  • \cos ^{ -1 }{ \left( \cfrac { 15 }{ \sqrt { 21 } \sqrt { 11 } } \right) }
A line d.c's proportional to (2,1,2) meets each of the lines x=y+a=z and x+a=2y=2z. Then the coordinates of each of the points of intersection are given by
  • (3a,2a,3a); (a,a,2a)
  • (3a,2a,3a); (a,a,a)
  • (3a,3a,3a); (a,a,a)
  • (2a,3a,3a); (2a,a,a)
If \frac{x-14}{l}=\frac{y-2}{m}=\frac{z+1}{n} is the equation of the line through (1,2,-1) and (-1,0,1), then (l,m,n) is 
  • (-1,0,1)
  • (1,1,-1)
  • (1,2,-1)
  • (0,1,0)
If A = (1,2,3) , B  = (2,10,1), Q are collinear points and Q_{x}=-1 then Q_{z} is
  • -3
  • 7
  • -14
  • -7
The direction cosines to two lines at right angles are (1,2,3) and (-2,\frac{1}{2},\frac{1}{3}), then the direction cosine perpendicular to both given lines are:
  • \sqrt{\frac{25}{2198}},\sqrt{\frac{19}{2198}},\sqrt{\frac{729}{2198}}
  • \sqrt{\frac{24}{2198}},\sqrt{\frac{38}{2198}},\sqrt{\frac{730}{2198}}
  • \frac{1}{3},-2,\frac{-7}{2}
  • None of the above
The direction cosines of a vector  \overrightarrow { A }  are \cos \alpha = \frac {4} { 5 \sqrt {2}} , \cos\beta =\frac { 1 }{ \sqrt { 2 }  } , \cos\gamma =\frac { 3 }{ 5\sqrt { 2 }  }  then, the vector \overrightarrow {A} is 
  • 4\hat { i } +\hat { j } +3\hat { k }
  • 4\hat { i } +5\hat { j } +3\hat { k }
  • 4\hat { i } -5\hat { j } +3\hat { k }
  • 4\hat { i } -\hat { j } -3\hat { k }
If  \bar { a }, \bar { b }, \bar { c } are non-coplaner vector , then the vectors 2\bar { a }- 4\bar { b }+ 4\bar { c }, \bar { a }- 2\bar { b }+ 4\bar { c } and -\bar { a }+ 2\bar { b }+ 4\bar { c } are parellel.
  • True
  • False
The angle between the lines \frac{{x - 2}}{3} = \frac{{y + 1}}{{ - 2}},z = 2 and \frac{{x - 1}}{1} = \frac{{2y + 3}}{3} = \frac{{z + 5}}{2} is equal to 
  • \pi /2
  • \pi /3
  • \pi /6
  • none of these
The direction ratios of the line joining the points (4, 3, -5) and (-2, 1, -8) are
  • \dfrac{6}{7}, \dfrac{2}{7}, \dfrac{3}{7}
  • 6, 2, 3
  • 5,8,0
  • 3,7,9
If \left(\dfrac {1}{2},\dfrac {1}{3},n\right) are the direction cosines of a line then the value of n is
  • \dfrac {\sqrt {23}}{6}
  • \dfrac {23}{6}
  • \dfrac {2}{3}
  • \dfrac {3}{2}
The angle between the pair of lines with direction ratios (1, 1, 2) and (\sqrt{3} - 1, -\sqrt{3} - 1, 4) is 
  • 30^o
  • 45^o
  • 60^o
  • 90^o
A line makes angles \alpha,\beta,\gamma,\delta with the four diagonals of a cube then \cos^{2}\alpha+\cos^{2}\beta+\cos^{2}\gamma+\cos^{2}\delta is equal to
  • 1
  • 4/3
  • 3/4
  • 4/5
The direction ratios of the line, given by the planes x - y + z - 5 = 0, x - 3y - 6 = 0 are 
  • (3, 1, -2)
  • (2, -4, 1)
  • (1,-1, 1)
  • (0,2,1)
If \overline { O A } = 3 \overline { i } + \overline { j } - \overline { k }, | \overline { A B } | = 2 \sqrt { 6 } and AB has the direction ratios 1, -1 , 2 then | O B | = 
  • \sqrt { 35 }
  • \sqrt { 41 }
  • \sqrt { 26 }
  • \sqrt { 55 }
The direction cosines of a vector A are \cos { \alpha  } =\frac { 4 }{ 5\sqrt { 2 }  } , cos \beta =\frac { 1 }{ \sqrt { 2 }  } , and cos \gamma = \frac{ 3 }{ 5\sqrt { 2 }  } , then vector A is
  • 4i+j+3k
  • 4i+5j+3k
  • 4i-5j-3k
  • none
The vector a = \alpha 1 + 2 j + \beta k lies in the plane of the vectors b = i + jt and c = j + k and bisects the angle between b and c. Then which one of the following gives possible values \alpha and \beta.
  • \alpha = 1 , \beta = 2
  • \alpha = 2 , \beta = 1
  • \alpha = 1 , \beta = 1
  • \alpha = 2 , \beta = 2
Let l_{1},\ m_{1},\ n_{1};\ l_{2},\ m_{2},\ n_{2};\ l_{3},\ m_{3},\ n_{3} be the direction cosines of three mutually perpendicular line then \begin{vmatrix} { l }_{ 1 } & m_{ 1 } & n_{ 1 } \\ { l }_{ 2 } & m_{ 2 } & n_{ 2 } \\ { l }_{ 3 } & m_{ 3 } & n_{ 3 } \end{vmatrix}
  • 0
  • \pm 1
  • \pm 2
  • \pm \dfrac{1}{2}
The point where \vec{ x } which is perpendicular to (2,-3,1) and (1,-2,3) and which satisfies the condition \vec { x } \cdot ( \hat { i } + 2 \hat { j } - 7 \hat{ k } ) = 10
  • \left(3,5,1\right)
  • \left(7,-5,1\right)
  • \left(3,-5,1\right)
  • \left(7,5,1\right)
The equation of the plane through \left(0,-5,1\right) which is perpendicular to the planes 2x+4y+2z+3=0,2x+5y+3z+4=0 is 
  • x+y+z=6
  • x-y+z=6
  • x-y-z=6
  • x+y+z+6=0
If A(p,q,r) and B=(p\prime ,q\prime ,r\prime ) are two points on the line \lambda x=\mu y=yz such that OA=3,OB=4 then pp\prime +qq\prime +rr\prime is equal to 
  • 7
  • 12
  • 5
  • None of these
The angle between the lines whose de's satisfy the equation l+m+m=0 and l^2+m^{2}-n^{2}=0 is 
  • \dfrac{\pi}{6}
  • \dfrac{\pi}{2}
  • \dfrac{\pi}{3}
  • \dfrac{\pi}{4}
The angle between the lines, whose direction ratios are 1,1,2 and \sqrt { 3 } - 1 , - \sqrt { 3 } - 1,4 , is
  • {45} ^ { \circ }
  • {30} ^ { \circ }
  • {60} ^ { \circ }
  • {90} ^ { \circ }
The directions cosines of the line which is perpedicular to the lines whose direction cosines are proportional to (1, -1, 2) and (2,-1,-1) are:
  • \dfrac { 1 }{ \sqrt { 35 } } ,-\dfrac { 5 }{ \sqrt { 35 } } \frac { 3 }{ \sqrt { 35 } }
  • -\dfrac { 1 }{ \sqrt { 35 } } ,\frac { 5 }{ \sqrt { 35 } } \dfrac { 3 }{ \sqrt { 35 } }
  • \dfrac { 1 }{ \sqrt { 35 } } ,\dfrac { 5 }{ \sqrt { 35 } } \frac { 3 }{ \sqrt { 35 } }
  • None of these
If a plane passes through the point (1, 1, 1) and is perpendicular to the line \dfrac{x-1}{3}=\dfrac{y-1}{0}=\dfrac{z-1}{4} then its perpendicular distance from the origin is 
  • \dfrac{3}{4}
  • \dfrac{4}{3}
  • \dfrac{7}{5}
  • 1
The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as l_{1},m_{1},n_{1};l_{2},m_{2},n_{2} and l_{3},m_{3},n_{3} are
  • l_{1}+ l_{2}+ l_{3},m_{1}+m_{2}+m_{3},n_{1}+n_{2}+n_{3}
  • \dfrac{l_{1}+l_{2}+l_{3}}{\sqrt{3}},\dfrac{m_{1}+m_{2}+m_{3}}{\sqrt{3}},\dfrac{n_{1}+n_{2}+n_{3}}{\sqrt{3}}
  • \dfrac{l_{1}+l_{2}+l_{3}}{3},\dfrac{m_{1}+m_{2}+m_{3}}{3},\dfrac{n_{1}+n_{2}+n_{3}}{3}
  • None\ of\ these
l=m=n=1 represent the direction cosines of the 
  • x- axis
  • y- axis
  • z- axis
  • none\ of\ these
If the points (p. 0), (0, q) and (1, 1) are collinear then \dfrac { 1 }{ p } +\dfrac { 1 }{ q } is equal to 
  • -1
  • 1
  • 2
  • 0
The direction ratios of the line
x-y+z-5=\quad 0\quad =\quad x-3y-6\quad are
  • 3,1,-2
  • 2,-4,1
  • \frac { 3 }{ \sqrt { 14 } } ,\frac { 1 }{ \sqrt { 14 } } ,\frac { -2 }{ \sqrt { 14 } }
  • \frac { 2 }{ \sqrt { 41 } } ,\frac { -4 }{ \sqrt { 41 } } ,\frac { 1 }{ \sqrt { 41 } }
The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as l_1, m_1, n_1 : l_2, m_2, n_2 and   l_3, m_3, n_3 are
  • l_1+l_2+l_3, m_1+m_2+m_3, n_1+n_2+n_3
  • \dfrac{l_1+l_2+l_3}{\sqrt{3}} , \dfrac{m_1+m_2+m_3}{\sqrt{3}} , \dfrac{n_1+n_2+n_3}{\sqrt{3}}
  • \dfrac{l_1+l_2+l_3}{3} , \dfrac{m_1+m_2+m_3}{3} , \dfrac{n_1+n_2+n_3}{3}
  • None of these
If  A(3\hat { i } +2\hat { j } +3\hat { k } ),B(-\hat { i } -\hat { j } +8\hat { k } ),C(-4\hat { i } +4\hat { j } +6\hat { k } )  are the vertices of a triangle then the equation of the line passing through the circumcentre and parallel to  \vec { A B }  is
  • \hat { r } =\left( -\dfrac { 4 }{ 3 } \hat { i } +\dfrac { 5 }{ 3 } \hat { j } +\dfrac { 17 }{ 3 } \hat { k } \right) +t(2\hat { i } +3\hat { j } -5\hat { k } )
  • \hat { r } =\left( \dfrac { 4 }{ 3 } \hat { i } +\dfrac { 5 }{ 3 } \hat { j } +\dfrac { 17 }{ 3 } \hat { k } \right) +t(2\hat { i } +3\hat { j } -5\hat { k } )
  • \hat { r } =\left( -\dfrac { 4 }{ 3 } \hat { i } +\dfrac { 5 }{ 3 } \hat { j } -\dfrac { 17 }{ 3 } \hat { k } \right) +t(2\hat { i } +3\hat { j } -5\hat { k } )
  • \hat { r } =\left( \dfrac { 4 }{ 3 } \hat { i } -\dfrac { 5 }{ 3 } \hat { j } +\dfrac { 17 }{ 3 } \hat { k } \right) +t(2\hat { i } +3\hat { j } -5\hat { k } )
The cartesian from of equation a line passing through the point position vector 2\hat{i}-\hat{j}+2\hat{k} and is in the direction of -2\hat{i}+\hat{j}+\hat{k}, is
  • \dfrac{x-2}{-2}=\dfrac{y+1}{1}=\dfrac{z-2}{1}
  • \dfrac{x+4}{-2}=\dfrac{y-1}{1}=\dfrac{z+2}{1}
  • \dfrac{x+2}{4}=\dfrac{y-1}{-1}=\dfrac{z-1}{2}
  • None \ of \ these
If \cos { \alpha ,\quad \cos { \beta ,\quad \cos { \gamma  }  }  }   are the direction cosine of a line, then find the value of { cos }^{ 2 }\alpha +\left( \cos { \beta +\sin { \gamma  }  }  \right)\left( \cos { \beta - \sin { \gamma  } }  \right)
  • 2
  • 0
  • -1
  • 1
\dfrac { x - 2 } { 1 } = \dfrac { y - 3 } { 1 } = \dfrac { z - 4 } { - 1 } & \dfrac { x - 1 } { k } = \dfrac { y - 4 } { 2 } = \dfrac { z - 5 } { 2 } are coplanar then k=?
  • any value
  • exactly one value
  • exactly 2 values
  • exactly 3 values
The plane through (1, 1, 1) (1, -1, 1) and (-7, -3, -5) is
  • Parallel to x-axis.
  • Parallel to y-axis.
  • Perpendicular to y-axis.
  • Perpendicular to x-axis.
Direction ratio of line given by \dfrac { x-1 }{ 3 } =\dfrac { 6-2y }{ 10 } =\dfrac { 1-z }{ -7 } are:
  • <3,10,-7>
  • <3,-5,7>
  • <3,5,7>
  • <3,5,-7>
A normal to the plane   x=2  is...
  • (0,1,1)
  • (2,0,2)
  • (1,0,0)
  • (0,1,0)
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers