CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 6 - MCQExams.com

Let the distance between vectors are given as follows :
$$(i)4i +3j-6k, -2i+j-k$$  be $$\displaystyle \sqrt{k}$$
$$(ii) -2i+3j+5k, 7i-k $$  be  $$\displaystyle m\sqrt{n}$$
Find $$k-(m*n)$$ ?
  • 20
  • 21
  • 22
  • 23
$$A, B, C$$ are three points on the axes of $$x, y$$ and $$z$$ respectively at distance $$a, b, c$$ from the origin $$O$$; then the co - ordinates of the point which is equidistant from $$A, B, C$$ and $$O$$ is
  • $$\displaystyle \left ( a,b,c \right )$$
  • $$\displaystyle \left ( \frac{a}{2},\frac{b}{2},\frac{c}{2} \right )$$
  • $$\displaystyle \left ( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right )$$
  • None of these
If the centroid of the tetrahedron $$OABC$$, where $$A, B ,C$$ are given by $$\displaystyle (\alpha, 5, 6), (1, \beta, 4), (3, 2, \gamma)$$ respectively be $$1, -1, 2$$, then value of $$\displaystyle \alpha^2 + \beta^2 + \gamma^2$$ equals
  • $$\displaystyle \alpha^2 + \beta^2$$
  • $$\displaystyle \gamma^2 + \beta^2$$
  • $$\displaystyle \alpha^2 + \gamma^2$$
  • None of these
Perimeter of triangle whose vertices are $$(0,4,0), (3,4,0)$$ and $$(0,4,4)$$, is
  • $$10$$
  • $$12$$
  • $$25$$
  • $$15$$
If $$P(x,y,z)$$ is a point on the line segment joining $$A (2,2,4)$$ and $$B(3,5,6)$$ such that projection of $$\vec{OP}$$ on axes are $$\displaystyle \frac{13}{5},\frac{19}{5},\frac{26}{5}$$ respectively, then P divide AB in the ratio
  • $$3:2$$
  • $$2:3$$
  • $$1:2$$
  • $$1:3$$
Find the ratio in which the yz-plane divides the join of the points $$\displaystyle \left ( -2,4,7 \right )$$ and $$\displaystyle \left ( 3,-5,8 \right )$$ and also find the co-ordinates of the point of intersection of this line with the $$yz$$ - plane.
  • $$\displaystyle \lambda =\frac{2}{3}$$ and $$\displaystyle \left ( 0,\frac{2}{5},\frac{37}{5} \right )$$
  • $$\displaystyle  \lambda =\frac{1}{3}$$ and $$\displaystyle \left ( \frac{-3}{4},\frac{7}{4},\frac{29}{4} \right )$$
  • $$\displaystyle  \lambda =\frac{2}{3}$$ and $$\displaystyle \left ( \frac{-3}{4},\frac{7}{4},\frac{29}{4} \right )$$
  • $$\displaystyle \lambda =\frac{1}{3}$$ and $$\displaystyle \left ( 0,\frac{2}{5},\frac{37}{5} \right )$$

Find the distance between the points whose position vectors are given as follows

$$-2\hat i+3\hat j+5\hat k, 7\hat i-\hat k$$
  • $$\displaystyle 3\sqrt{14}$$
  • $$\displaystyle \sqrt{54}$$
  • $$\displaystyle 3\sqrt{19}$$
  • $$\displaystyle \sqrt{57}$$
The points $$A(5, 1, 1), B(7, 4, 7), C(1, 6, 10)$$ and $$D(-1, 3, 4)$$ are the vertices of a
  • Parallelogram
  • Rectangle
  • Rhombus
  • Square
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 projection of $$\overline { OP } $$ on the axes are $$\displaystyle\frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } ,$$ respectively, then $$P$$ divides $$QR$$ in the ratio
  • $$1:2$$
  • $$3:2$$
  • $$2:3$$
  • $$1:3$$
Find the distance between the points whose position vectors are given as follows
$$(-1,1,3), (0,5,6)$$
  • $$\displaystyle \sqrt{118}$$
  • $$8$$
  • $$\displaystyle \sqrt{26}$$
  • none of these
The plane $$XOZ$$ divides the join of $$(1, - 1, 5)$$ and $$(2, 3, 4)$$ in the ratio $$\lambda : 1$$, then $$\lambda$$ is -
  • $$- 3$$
  • $$-1 / 3$$
  • $$3$$
  • $$1 / 3$$
Find the distance between the pairs of points whose cartesian coordinates are $$(2,3,-1), (2,6,2).$$
  • $$\displaystyle 3\sqrt{2}.$$
  • $$\displaystyle 2\sqrt{3}.$$
  • $$\displaystyle 5\sqrt{2}.$$
  • $$\displaystyle 2\sqrt{5}.$$
Find the distance between the points whose position vectors are given as follows
$$4\hat i+3\hat j-6\hat k, -2\hat i+\hat j-\hat k$$
  • $$\displaystyle \sqrt{65}$$
  • $$\displaystyle \sqrt{69}$$
  • $$13$$
  • none of these
Find the point which divides the lines joining $$A(2,3,5)$$ and $$B(-6,5,8)$$ in the ratio $$2:3$$ externally
  • $$(18,-1,-1)$$
  • $$(12,-1,-1)$$
  • $$(3,4,4)$$
  • $$(5,8,11)$$
The ordinate of the point which divides the lines joining the origin and the point $$(1,2)  $$ externally in the ratio of $$3:2$$ is
  • $$-2$$
  • $$ \displaystyle \frac{3}{5} $$
  • $$ \displaystyle \frac{2}{5} $$
  • $$6$$
Find the ratio in which (the plane) $$2x+3y+5z=1$$ divides the line joining the points $$(1,0,-3)$$ and $$(1,-5,7)$$.
  • $$1:2$$
  • $$2:3$$
  • $$3:1$$
  • None of these
A hall has dimensions $$24 m \times 8 m \times 6 m$$. The length of the longest pole which can be accommodated in the hall is
  • 26 m
  • 28 m
  • 30 m
  • 36 m
The coordinates of a point which divides the line joining the points $$P(2,3,1)$$ and $$Q(5,0,4)$$ in the ratio $$1:2$$ are
  • $$\left(\dfrac{7}{3}, 1, \dfrac{5}{3}\right)$$
  • $$(4, 1, 3)$$
  • $$(3, 2, 2)$$
  • $$(1, -1, 1)$$
In $$\triangle ABC$$ the mid points of the sides $$AB, BC$$ and $$CA$$ are respectively $$\left( l,0,0 \right) ,\left( 0,m,0 \right) $$ and $$\left( 0,0,n \right) $$. Then, $$\dfrac { { AB }^{ 2 }+{ BC }^{ 2 }+{ CA }^{ 2 } }{ { l }^{ 2 }+{ m }^{ 2 }+{ n }^{ 2 } } $$ is equal to
  • $$2$$
  • $$4$$
  • $$8$$
  • $$16$$
The distance of the point (1,−2,4) from the plane passing through the point (1,2,2) and perpendicular to the planes $$x−y+2z=3$$ and $$2x−2y+z+12=0$$ is :
  • $$2\sqrt{2}$$
  • $$4$$
  • $$\sqrt2$$
  • $$23$$
The coordinates of any point, which lies in $$yz$$ plane, are
  • $$(x,y,y)$$
  • $$(0,y,y)$$
  • $$(0,y,x)$$
  • $$(x,y,z)$$
The point $$(3, 0, -4)$$ lies on the
  • Y-axis
  • Z-axis
  • XY-plane
  • XZ-plane
  • YZ-plane
What is the length of the segment in the x-y plane with end points at $$(-2, -2)$$ and $$(2, 3)$$?
  • $$3$$
  • $$\sqrt{31}$$
  • $$\sqrt{41}$$
  • $$7$$
  • $$9$$
If the line joining $$A(1, 3, 4)$$ and $$B$$ is divided by the point $$(-2, 3, 5)$$ in the ratio $$1 : 3$$, then $$B$$ is
  • $$(-11, 3, 8)$$
  • $$(-11, 3, -8)$$
  • $$(-8, 12, 20)$$
  • $$(13, 6, -13)$$
Graph $$x^2+y^2=4$$ in 3D looks like
  • Circle
  • Cylinder
  • Hemisphere
  • Sphere
An equation of sphere with centre at origin and radius $$r$$ can be represented as
  • $$x^2+y^2+z^2=r$$
  • $$x^2+y^2+z^2=r^2$$
  • $$x^2+y^2+z^2=2r^2$$
  • None of the above
Point $$D$$ has coordinates as $$(3,4,5)$$. Referring to the given figure, find the coordinates of point $$E$$.
505625.png
  • $$(0,4,3)$$
  • $$(0,4,5)$$
  • $$(0,5,4)$$
  • $$(0,3,4)$$
The ratio in which the line joining $$(2, -4, 3)$$ and $$(-4, 5, -6)$$ is divided by the plane $$3x+2y+z-4=0$$ is
  • $$2 : 1$$
  • $$4 : 3$$
  • $$-1 : 4$$
  • $$2 : 3$$
Calculate the distance between the points $$(-3,6,7)$$ and $$(2,-1,4)$$ in $$3D$$ space.
  • $$4.36$$
  • $$5.92$$
  • $$7.91$$
  • $$9.11$$
  • $$22.25$$
If the distance between the points $$(7,1,-3)$$ and $$(4,5,\lambda)$$ is $$13$$ units, then what is one of the values of $$\lambda$$?
  • $$20$$
  • $$10$$
  • $$9$$
  • $$8$$
0:0:1


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