CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 3 - MCQExams.com

If the extremities of a diagonal of a square are $$(1, -2, 3)$$ and $$(2, -3, 5)$$, then area of the square is
  • $$6$$
  • $$3$$
  • $$\displaystyle \dfrac{3}{2}$$
  • $$\sqrt{3}$$

$$A=(2, 4, 5)$$ and $$B=(3,5, -4)$$ are two points. lf the $$XY$$-plane, $$YZ$$-plane divide $$AB$$ in the ratio $$a:b$$ and $$ p:q$$ respectively, then $$\dfrac {a}{b}+\dfrac {p}{q}=$$
  • $$\displaystyle \dfrac{23}{12}$$
  • $$\displaystyle \dfrac{-7}{12}$$
  • $$\displaystyle \dfrac{7}{12}$$
  • $$\displaystyle \dfrac{-22}{15}$$
If $$A= (1, 2, 3), B = (2, 3, 4)$$ and $$AB$$ is produced upto $$C$$ such that $$2AB = BC$$, then $$C =$$
  • $$(5, 4, 6)$$
  • $$(6, 2, 4)$$
  • $$(4, 5, 6)$$
  • $$(6, 4, 5)$$
If the points $$A(3, -2, 4)$$, $$B(1, 1, 1)$$ and $$C(-1, 4, -2)$$ are collinear, then the ratio in which $$C$$ divides $$AB$$ is 
  • $$1 : 2$$
  • $$-2 :1$$
  • $$-1 : 2$$
  • $$4 : 0$$
Two opposite vertices of a square are $$(2, -3, 4)$$ and $$(4, 1, -2)$$. The length of the side of the square is
  • $$\sqrt{58}$$
  • $$2\sqrt{7}$$
  • $$\sqrt{14}$$
  • $$\sqrt{7}$$
If $$A = (2, -3, 1), B = (3, -4, 6)$$ and $$C$$ is a point of trisection of $$AB$$, then $${C}_{{y}}=$$
  • $$\displaystyle \dfrac{11}{3}$$
  • $$-11$$
  • $$\displaystyle \dfrac{10}{3}$$
  • $$\displaystyle \dfrac{-11}{3}$$
The point $$P$$ is on the $$y$$-axis. If $$P$$ is equidistant from $$(1,2, 3)$$ and $$(2,3, 4)$$, then $$P_{y}=$$
  • $$\displaystyle \dfrac{15}{2}$$
  • $$15$$
  • $$30$$
  • $$\displaystyle \dfrac{3}{2}$$
$$A = (1, -2, 3)$$ , $$B =$$ (2, 1, 3), $$C =$$ (4, 2, 1) and $$G= (-1,3, 5)$$ is the centroid of the tetrahedron $$ABCD$$. Then the fourth coordinate is
  • $$(11,11,13)$$
  • $$(-11,11,45)$$
  • $$(-11,11,13)$$
  • $$(11,13,11)$$
$$XOZ$$ plane divides the join of $$(2,3,1)$$ and $$(6,7,1)$$ in the ratio
  • $$3: 7$$
  • $$2 : 7$$
  • $$-3 : 7$$
  • $$-2 : 7$$
The shortest distance of $$(a,b,c)$$ from $$x$$-axis is
  • $$\sqrt{\mathrm{a}^{2}+b^{2}}$$
  • $$\sqrt{b^{2}+\mathrm{c}^{2}}$$
  • $$\sqrt{\mathrm{c}^{2}+\mathrm{a}^{2}}$$
  • $$\sqrt{\mathrm{a}^{2}+b^{2}+\mathrm{c}^{2}}$$
The distance between the circumcentre and the ortho centre of the triangle formed by the points $$(2, 1, 5), (3, 2, 3)$$ and $$(4, 0, 4)$$ is
  • $$\sqrt{6}$$
  • $$\displaystyle \dfrac{\sqrt{6}}{2}$$
  • $$2\sqrt{6}$$
  • $$0$$
If the $$zx$$-plane divides the line segment joining $$(1, -1, 5)$$ and $$(2, 3, 4)$$ in the ratio $$p : 1$$, then $$p + 1=$$
  • $$\displaystyle \dfrac{1}{3}$$
  • $$1 $$
  • $$\displaystyle \dfrac{3}{4}$$
  • $$\displaystyle \dfrac{4}{3}$$
The ratio in which $$yz$$-plane divides the line segment joining $$(-3, 4, 2), (2, 1, 3)$$ is
  • $$-4 : 1$$
  • $$3 : 2$$
  • $$-2 : 3$$
  • $$1: 4$$
If $$(4, 2, p)$$ is the centroid of the tetrahedron formed by the points $$(k, 2, -1), (4, 1, 1), (6,2, 5)$$ and
$$(3, 3, 3)$$ then $$k + p=$$
  • $$\displaystyle \frac{17}{3}$$
  • $$1$$
  • $$\displaystyle \frac{5}{3}$$
  • $$5$$
The circum centre of the triangle formed by the points $$(2, 5, 1), (1, 4, -3)$$ and $$(-2, 7, -3)$$ is
  • $$(6,0,1)$$
  • $$(0,6,-1)$$
  • $$(-1,6,2)$$
  • $$(6,1,-2)$$
The distance from the origin to the centroid of the tetrahedron formed by the points $$(0, 0, 0), (a, 0, 0), (0, b, 0), (0, 0, c)$$ is:
  • $$\displaystyle \dfrac{\sqrt{a+{b}+{c}}}{4}$$
  • $$\displaystyle \dfrac{\sqrt{{a}+{b}+{c}}}{3}$$
  • $$\displaystyle \dfrac{\sqrt{{a}^{2}+{b}^{2}+{c}^{2}}}{16}$$
  • $$\displaystyle \dfrac{\sqrt{{a}^{2}+{b}^{2}+{c}^{2}}}{4}$$
The circum radius of the triangle formed by the points $$(1, 2, -3), (2, -3, 1)$$ and $$(-3, 1, 2)$$ is:
  • $$\sqrt{14}$$
  • $$14$$
  • $$\sqrt{13}$$
  • $$0$$
$$G(1, 1, -2)$$ is the centroid of the triangle $$ABC$$ and $$D$$ is the mid point of $$BC$$. If $$A = (-1, 1, -4)$$, then $$D =$$
  • $$\left (\displaystyle \dfrac{1}{2},1, \dfrac{-5}{2}\right)$$
  • $$(5,1,2)$$
  • $$(-5,-1,-2)$$
  • $$(2,1, -1)$$
If the centroid of tetrahedron $$OABC$$ where $$A,B,C$$ are given by $$(a,2,3), (1,b,2)$$ and $$(2,1,c)$$ respectively is $$(1,2,-2)$$, then distance of $$P(a,b,c)$$ from origin is
  • $$\sqrt{195}$$
  • $$\sqrt{14}$$
  • $$\sqrt{\dfrac{107}{14}}$$
  • $$\sqrt{13}$$
The circum radius of the triangle formed by the points $$(2, -1, 1), (1, -3, -5)$$ and $$(3, -4, -4)$$ is
  • $$\displaystyle \dfrac{\sqrt{6}}{2}$$
  • $$\displaystyle \dfrac{\sqrt{35}}{2}$$
  • $$\displaystyle \dfrac{\sqrt{41}}{2}$$
  • $$\sqrt{41}$$
If $$\mathrm{A}= (-1,6, 6)$$ , $$\mathrm{B}=(-4,9, 6)$$ , $$\displaystyle \mathrm{G}=\frac{1}{3}(-5,22,22)$$ and $$\mathrm{G}$$ is the centroid of the $$\Delta \mathrm{A}\mathrm{B}\mathrm{C}$$ then the name of the triangle $$\mathrm{A}\mathrm{B}\mathrm{C}$$ is
  • an isosceles triangle
  • a right angled triangle
  • an equilateral triangle
  • a right-angled isosceles triangle
If the orthocentre, circumcentre of a triangle are $$(-3, 5, 2), (6, 2, 5)$$ respectively then the centroid of the triangle is
  • $$(3,3, 4)$$
  • $$\left (\displaystyle \dfrac{3}{2},\dfrac{7}{2},\dfrac{9}{2}\right)$$
  • $$(9,9,12)$$
  • $$\left (\displaystyle \dfrac{9}{2}\dfrac{-3}{2},\dfrac{3}{2}\right)$$
The extremities of a diagonal of a rectangular parallelopiped whose faces are parallel to the reference planes are $$(-2, 4, 6)$$ and $$(3, 16, 6)$$. The length of the base diagonal is
  • $$7$$
  • $$10$$
  • $$11$$
  • $$13$$
In the tetrahedron $$ABCD,\ A= (1, 2, -3)$$ and $$G(-3,4, 5)$$ is the centroid of the tetrahedron. If $$P$$ is the centroid of the $$\Delta BCD$$, then $$AP=$$
  • $$\displaystyle \dfrac{8\sqrt{21}}{3}$$
  • $$\displaystyle \dfrac{4\sqrt{21}}{3}$$
  • $$4\sqrt{21}$$
  • $$\displaystyle \dfrac{\sqrt{21}}{3}$$
In the $$\Delta $$ ABC , A $$=$$ (1, 3, -2) and G (-1, 4, 2) is the centroid of the triangle. If D is the mid point of BC then AD $$=$$
  • $$\displaystyle \dfrac{\sqrt{21}}{2}$$
  • $$\displaystyle \dfrac{3\sqrt{21}}{2}$$
  • $$\sqrt{21}$$
  • $$\dfrac{63}{2}$$
The harmonic conjugate of $$(2, 3, 4)$$ with respect to the points $$(3, -2, 2)$$ and $$(6, -17, -4)$$ is
  • $$(\dfrac{18}{5}, -5,\dfrac{4}{5})$$
  • $$(11, -16,2)$$
  • $$\left (\displaystyle \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}\right)$$
  • $$(0, 0, 0)$$
$$A = (2, 3, 0)$$ and $$B = (2,1, 2)$$ are two points. If the points $$P, Q$$ are on the line $$AB$$ such that $$AP= PQ = QB$$, then $$PQ=$$
  • $$2\sqrt{2}$$
  • $$6\sqrt{2}$$
  • $$\sqrt{\dfrac{8}{9}}$$
  • $$\sqrt{2}$$
Then the correct matching is
List - I
List - II
A: The coordinates of the
mid point of the line joining

$$(-1,-1,1)$$ and $$(-1,1,-1)$$


1) $$(-2,1,1)$$

B: The coordinates of the
point which divides the
line segment joining

$$($$2,3,1 $$)$$ and $$(5, 0,4)$$
in the ratio1:2


2) $$(-1,0,0)$$


$$\mathrm{C}$$: The points and $$P(2,1, -3)$$
are three vertices of a
parallelogram $$\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$$,
the fourth vertex


 3) $$(\displaystyle \frac{13}{3},\frac{-11}{3},6)$$


$$\mathrm{D}$$: The vertices of a triangle
are $$(7,-4,7)$$ , $$(1,-6,10)$$
and $$(5, -1,1)$$ . centroid of the
triangle

4) $$($$3, 2, 2 $$)$$
  • $$A-2,\ B-4,\ C-1,\ D-3$$
  • $$A-1,\ B-2,\ C-3,\ D-4$$
  • $$A-2,\ B-3,\ C-1,\ D-4$$
  • $$A-1,\ B-4,\ C-3,\ D-2$$
If the points $$A,B,C,D$$ are collinear and $$C,D$$ divide $$AB$$ in the ratios $$2:3, -2:3$$ respectively, then the ratio in which $$A$$ divides $$CD$$ is
  • $$5:1$$
  • $$2:3$$
  • $$3:2$$
  • $$1:5$$

$$P (1,1,1 )$$ and $$Q(\lambda, \lambda, \lambda)$$ are two points in the space such that $$PQ=\sqrt{27}$$, then the value(s) of $$\lambda $$ can be
  • $$-4$$
  • $$-2,4$$
  • $$2$$
  • $$4,3$$
0:0:1


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