CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 11 - MCQExams.com

If $$P\left( x,y,z \right) $$ is a point on the line segment joining $$Q\left( 2,2,4 \right) $$ and $$R\left( 3,5,6 \right) $$ such that the projections of $$OP$$ on the axis are $$\cfrac { 13 }{ 5 } ,\cfrac { 19 }{ 5 } ,\cfrac { 26 }{ 5 } $$ respectively, then $$P$$ divides $$QR$$ in the ratio
  • $$1:2$$
  • $$3:2$$
  • $$2:3$$
  • $$1:3$$
The points $$A(1,2,3); B-(-1,-2,-1); C(2,3,2)$$ and $$D(4,7,6)$$ form 
  • Square
  • Rectangle
  • Parallelogram
  • Rhombus
Find the coordinates of the points which trisect the line segment AB, given that A =( 2,1 , - 3 ) and  B =( 5 , - 8,3 ).
  • $$( 3,2 , - 1 ) ; ( 4,5 , - 1 )$$
  • $$( 3 , - 2 , - 1 ) ; ( 4 , - 5,1 )$$
  • $$( 3 , - 2,1 ) ; ( - 4,5 , - 1 )$$
  • $$( 3 , - 2 , - 1 ) ; ( 4,5 , - 1 )$$
30 consider at three dimensional figure represented by $$xy{z^2} = 2$$, then its minimum distance from origin is 
  • 2
  • 4
  • 3
  • 1
The distances of the point $$P(1,2,3)$$ from the coordinates axes are:
  • $$\sqrt {13} ,\sqrt {10} ,\sqrt 5 $$
  • $$\sqrt {11} ,\sqrt {10} ,\sqrt 5 $$
  • $$\sqrt {13} ,\sqrt {20} ,\sqrt {15} $$
  • $$\sqrt {23} ,\sqrt {10} ,\sqrt 5 $$
If O and O' are circumcenter and orthocenter of a $$\Delta ABC$$ where $$\overline{OA} + \overline{OB} + \overline{OC}$$ is $$\lambda \overline{OO'}$$ then the value of $$\lambda$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The distance between the orthocentre and circumcentre of the triangle formed by the points $$(1, 2, 3), (3, -1, 5), (4, 0, -3)$$ is
  • $$\dfrac {\sqrt {66}}{2}$$
  • $$\dfrac {\sqrt {17}}{2}$$
  • $$\dfrac {\sqrt {55}}{2}$$
  • $$\dfrac {\sqrt {37}}{2}$$
In the $$xy-plane$$, the length of the shortest from $$(0, 0)$$ to $$(12, 16)$$ that does not go inside the circle $$(x - 6)^{2} + (y + 8)^{2} = 25$$ is
  • $$10\sqrt {3}$$
  • $$10\sqrt {5}$$
  • $$10\sqrt {3} + \dfrac {5\pi}{3}$$
  • $$10 + 5\pi$$
If $$R$$ divides the line segment joining $$P(2,3,4)$$ and $$Q(4,5,6)$$ in the ratio $$-3:2$$, then the parameter which represent $$R$$ is 
  • $$3$$
  • $$2$$
  • $$1$$
  • $$-1$$
Consider at three dimensional figure represented by $$xy{ z }^{ 2 }=2$$, then its minimum distance from origin is
  • 2
  • 4
  • 6
  • 8
The point which is equidistant from the points $$(-1,1,3),(2,1,2),(0,5,6)$$ and $$(3,2,2)$$ is
  • $$(-1,3,4)$$
  • $$(3,1,4)$$
  • $$(1,3,4)$$
  • $$(4,1,3)$4
Minimum distance between the curves
$$y^{2}=4x$$ & $$x^{2}+y^{2} -12x+31=0$$ is -
  • $$\sqrt {21}$$
  • $$\sqrt {26}-\sqrt {5}$$
  • $$\sqrt {20}-\sqrt {5}$$
  • $$\sqrt {21}-\sqrt {5}$$
Let $$A(2,3,5),B(-1,3,2)$$ and $$C(\lambda ,5,\mu )$$ are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that $$BE:EC=1:2.$$
Project of BA on BC
  • $$\dfrac { 23 }{ \sqrt { 33 } } $$
  • $$\dfrac { \sqrt { 33 } }{ 24 } $$
  • $$\dfrac { 24 }{ \sqrt { 33 } } $$
  • $$None$$ $$of$$ $$these$$
If A = (2,-3,1), B = (3,-4,6) and C is a point of trisection of AB, then $${ C }_{ y }$$
  • $$\frac { 11 }{ 3 } $$
  • -11
  • $$\frac { 10 }{ 3 } $$
  • $$\frac { -11 }{ 3 } $$
The coordinates of the orthocentre of the triangle that has the coordinates of mid points of its sides as (0 , 0) (1 , 2) and ( -6 , 3) is : 
  • (0 , 0)
  • (-4 , 5)
  • (-5 , 5)
  • (-4 , 4)
Let $$A(2,3,5),B(-1,3,2)$$ and $$C(\lambda ,5,\mu )$$ are the vertices of a triangle and its median through A meets side BC at D. AD is equally inclined with the axes. If E is the point on BC such that $$BE:EC=1:2.$$
Equation of plane containing triangle ABC
  • $$x+y+3=0$$
  • $$x-z-3=0$$
  • $$x-z+3=0$$
  • $$x-y+3=0$$
Perpendicular distance from the origin to the line joining the points $$(a\cos{\theta},a\sin{\theta})(a\cos{\theta},a\sin{\theta})$$ is
  • $$2a\cos{(\theta-\phi)}$$
  • $$a\cos { \left( \cfrac { \theta -\phi }{ 2 } \right) } $$
  • $$4a\cos { \left( \cfrac { \theta -\phi }{ 2 } \right) } $$
  • $$a\cos { \left( \cfrac { \theta +\phi }{ 2 } \right) } $$
Consider a variable plane $$lx+my+nz=k(k>0)and\quad l,m,n$$ are direction cosines of normal of the plane. Let the given plane intersects the co-ordinate axes at A,B and C, then the minimum area of $$\triangle ABC$$ is _______.
  • $$\dfrac { 3\sqrt { 3k } ^{ 2 } }{ 2 } $$
  • $$\dfrac { 3\sqrt { 3k } ^{ 2 } }{ 4 } $$
  • $$3\sqrt { 3 } { k }^{ 2 }$$
  • $$12\sqrt { 3 } { k }^{ 2 }$$
The shortest distance between the point $$\left( \dfrac { 3 }{ 2 } ,0 \right) $$ and the curve $$y=\sqrt { x } $$, $$(x>0)$$, is:
  • $$\dfrac { 3 }{ 2 } $$
  • $$\dfrac { \sqrt { 3 } }{ 2 } $$
  • $$\dfrac { \sqrt { 5 } }{ 2 } $$
  • $$\dfrac { 5 }{ 4 } $$
Q, R, S are the points $$(-2, -1), (0, 3) (4, 0)$$ respectively. Then the coordinates of P such that PQRS is a parallelogram is ________________.
  • $$(2, -6)$$
  • $$(-6, 2)$$
  • $$(2, -4)$$
  • $$(-3, 2)$$
If $$A=(1, 2, 3)$$ and $$B(3, 5, 7)$$ and P, Q are the points on AB such that AP$$=$$PQ$$\neq$$QB, then the mid point of PQ is?
  • $$(2, 3, 5)$$
  • $$\left(2, \dfrac{7}{2}, 5\right)$$
  • $$(2, 4, 5)$$
  • $$(4, 7, 0)$$
If $$A=(1, -2, -1), B=(4, 0, -3); C=(1, 2, -1)$$ and $$D=(2, -4, -5)$$, then the distance between AB and CD is?
  • $$\dfrac{2}{3}$$
  • $$\dfrac{4}{3}$$
  • $$\dfrac{3}{2}$$
  • $$\dfrac{5}{3}$$
The equation of plane which is passing through the point $$(1,2,3)$$ and which is at maximum distance from the point $$(-1,0,2)$$ is
  • $$2x+2y+z=9$$
  • $$2x+z=5$$
  • $$3x+y-z=2$$
  • none of these
The distance of the point $$(2,1,-1)$$ from the line $$\dfrac{x-1}{2}=\dfrac{y+1}{1}=\dfrac{z-3}{-3}$$ measured parallel to the plane $$x+2y+z=4$$ is
  • $$\sqrt{10}$$
  • $$\sqrt{20}$$
  • $$\sqrt{5}$$
  • $$\sqrt{30}$$
A line passes through two points A(2, -3, -1) and B(8, -1, 2) the coordinates of a point on this line nearer to the origin at a distance of 14 units from A are  
  • (14 , 1, 5)
  • (-10, -7, -7)
  • (10 , 7, 7)
  • (-14, -1, -5)
If $$\lambda$$ is the length of any edge of a regular tetrahedron, then the distance of any vertex form the opposite face is-
  • $$\dfrac{2}{3}\lambda^{2}$$
  • $$\sqrt{\dfrac{2}{3}}\lambda$$
  • $$\dfrac{\sqrt{2}}{3}\lambda$$
  • $$None of these$$
The distance of the point $$(2,3)$$ form the line $$x-2y+5=0$$ measured in a direction parallel to the line $$x-3y=0$$ is
  • $$2\sqrt{10}$$
  • $$\sqrt{10}$$
  • $$2\sqrt{5}$$
  • $$None\ of\ these$$
If $$  A=(1,-2,-1), B=(4,0,-3), C=(1,2,-1), D=(2,-4,-5)  $$, then distance between A B and CD is
  • $$

    \frac{1}{3}

    $$
  • $$

    \frac{2}{3}

    $$
  • 1
  • $$

    \frac{4}{3}

    $$
$$A(1, -1, -3)$$, $$B(2,1,-2)$$ & $$(-5, 2, -6)$$ are the position vectors of the vertices of a triangle ABC. The length of the bisector of its internal angle at A is:
  • $$\sqrt { 10 } /4$$
  • $$3\sqrt { 10 } /4$$
  • $$\sqrt { 10 } $$
  • None
If x-coordinates of a point P on the joining the points $$Q(2, 2,1)$$ and $$R(5, 1, -2)$$ is 4, then the z-coordinates of P is
  • -2
  • -1
  • 1
  • 2
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers