CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 5 - MCQExams.com

If $$P= (0, 0, 0), Q = (3, 6, 9)$$ and $$R$$ is a point of trisection of $$PQ$$, then $$R_y=$$
  • $$\displaystyle \frac{4}{3}$$
  • $$2$$
  • $$3$$
  • $$9$$
If the distance of a point $$(a,a,a)$$ from the origin is $$ \sqrt { 108 } $$, then the value of $$a$$ is
  • $$9$$
  • $$6$$
  • $$-9$$
  • $$-6$$
Three vertices of a tetrahedron are $$(0, 0, 0), (6, -5, -1) $$ and $$(-4, 1, 3)$$. If the centroid of the tetrahedron be $$(1, -2, 5) $$ then the fourth vertex is
  • $$(2, -4, 18)$$
  • $$(1, -4, 18)$$

  • $$\left (\dfrac {3}{2}, \dfrac {-3}{2}, \dfrac {7}{4}\right )$$

  • none of these
A $$= (1, 1, 4)$$ and B $$= (5,-3, 4)$$ are two points. If the points $$P$$, $$Q$$ are on the line AB such that AP $$=$$ PQ $$=$$ QB then PQ $$=$$
  • $$2\sqrt{2}$$
  • $$4$$
  • $$\sqrt{\displaystyle \frac{32}{9}}$$
  • $$\sqrt{2}$$
If P $$(3, 2, -4)$$ , Q $$(5, 4, -6)$$ and R $$(9, 8, -10)$$ are collinear, then R divides PQ in the ratio
  • $$3 : 2$$ internally
  • $$3 : 2$$ externally
  • $$2 : 1$$ internally
  • $$2 : 1$$ externally
The distance from the origin to the centroid of the tetrahedron formed by the points $$(0, 0, 0), (3, 0, 0), (0, 4, 0), (0, 0, 5)$$ is 
  • $$\displaystyle \frac{\sqrt{\mathrm{3}+\mathrm{4}+\mathrm{5}}}{4}$$
  • $$\displaystyle \frac{\sqrt{\mathrm{3}+\mathrm{4}+\mathrm{5}}}{3}$$
  • $$\displaystyle \frac{\sqrt{\mathrm{3}^{2}+\mathrm{4}^{2}+\mathrm{5}^{2}}}{16}$$
  • $$\displaystyle \frac{\sqrt{\mathrm{3}^{2}+\mathrm{4}^{2}+\mathrm{5}^{2}}}{4}$$
The position vectors of the four angular point of a tetrahedron $$OABC$$ are $$(0, 0, 0)$$; $$(0, 0, 2)$$; $$(0, 4, 0)$$ and $$(6, 0, 0)$$ respectively. Find the coordinates of cenroid
  • $$\left (2, \displaystyle \frac {4}{3}, \displaystyle \frac {2}{3}\right )$$
  • $$\left (\displaystyle \frac {6}{4}, 1, \displaystyle \frac {2}{4}\right )$$
  • $$(0, 0, 0)$$
  • none of these
Let $$A= \left ( 1,2,3 \right )B= \left ( -1,-2,-1 \right )C= \left ( 2,3,2 \right )$$ and $$ D= \left ( 4,7,6 \right )$$. Then $$ABCD$$ is a
  • rectangle
  • square
  • parallelogram
  • none of these
If $$A= \left ( 5,-1,1 \right ),B= \left ( 7,-4,7 \right ),C= \left ( 1,-6,10 \right ),D= \left ( -1,-3,4 \right )$$. Then $$ABCD$$ is a
  • square
  • rectangle
  • rhombus
  • none of these
The equation of the plane which is parallel to the $$xy-$$plane is
  • $$x=y$$
  • $$z=c$$
  • $$y=c$$
  • $$z=xy$$
If  $$C_1:{x^2+y^2}-20x+64=0$$ and $$C_2:{x^2+y^2}+30x+144=0$$. Then the length of the shortest line segment $$PQ$$  which touches $$C_1$$ at $$P$$ and  to  $$C_2$$ at $$Q$$ is
  • $$10$$
  • $$15$$
  • $$22$$
  • $$27$$
The plane $$XOZ$$ divides the join of $$(1,-1,5)$$ and $$(2,3,4)$$ in the ratio $$\lambda :1$$, then $$\lambda$$ is
  • $$-3$$
  • $$\dfrac {1}{4}$$
  • $$3$$
  • $$\dfrac {1}{3}$$
The distance of the point $$(1,-2,3)$$ from  the plane $$x-y+z=5$$ measured parallel to the line $$\displaystyle \frac{x}{2}=\displaystyle \frac{y}{3}=\displaystyle \frac{z}{-6}$$ is
  • $$1$$
  • $$19$$
  • $$155$$
  • $$\sqrt{271}$$
The points $$A(1, 2, -1), B(2, 5, -2), C(4, 4, -3)$$ and $$D(3, 1, -2)$$ are
  • collinear
  • vertices of a rectangle
  • vertices of a square
  • vertices of a rhombus
A line passes through two point $$A (2, -3, -1)$$ and $$B (8, -1, 2)$$. The coordinates of a point on this line at a distance of $$14$$ units from $$A$$ are
  • $$(14, 1, 5)$$
  • $$(-10, -7, 7)$$
  • $$(86, 25, 41)$$
  • None of these
The chord of contact of tangents from a point $$P$$ to a circle passes  through $$q$$. If $$l_1$$ and $$l_2$$ are the lengths of the tangents from $$P$$ and $$Q$$ to the circle, then $$PQ$$ is equal to
  • $$\dfrac{l_1+l_2}{2}$$
  • $$\dfrac{l_1-l_2}{2}$$
  • $$\sqrt{|{l^2_1}-{l^2_2}|}$$
  • $$\sqrt[2]{{l^2_1}+{l^2_2}}$$
Find the coordinates of the point on the $$x$$-axis that is equidistant from $$P(4,3,1)$$ and $$Q(-2,-6,-2)$$.
  • $$\displaystyle \left( \frac { 3 }{ 2 } ,0,0 \right) $$
  • $$\displaystyle \left( - \frac { 3 }{ 2 } ,0,0 \right) $$
  • $$\displaystyle \left( 0,-\frac { 3 }{ 2 } ,0 \right) $$
  • $$\displaystyle \left( 0,\frac { 3 }{ 2 } ,0 \right) $$
If $$(1,-1,0),(-2,1,8)$$ and $$(-1,2,7)$$ are three consecutive vertices of a parallelogram then the fourth vertex is
  • $$(2,0,-1)$$
  • $$(1,0,-1)$$
  • $$(1,-2,0)$$
  • $$(0,-2,1)$$
If $$P(x,y,z)$$ is a point on the line segment joining $$Q(2,2,4)$$ and $$R(3,5,6)$$ such that the projection of $$\overrightarrow { OP } $$ on the axes are $$\displaystyle \frac { 13 }{ 5 } ,\frac { 19 }{ 5 } ,\frac { 26 }{ 5 } $$ respectively, then $$P$$ divides $$QR$$ in ratio
  • $$1:3$$
  • $$2:3$$
  • $$3:2$$
  • $$3:1$$
The distance of the point $$\left( 1,-2,3 \right) $$ from the plane $$x-y+z=5$$ measured parallel to the line $$\displaystyle \frac { x }{ 2 } =\frac { y }{ 3 } =\frac { z-1 }{ -6 } $$ is
  • $$1$$
  • $$2$$
  • $$4$$
  • None of these
The ratio in which the plane $$\displaystyle \bar {r} .(\bar {i} - 2 \bar {j} + 3 \bar {k}) = 17$$ divides the line joining the points $$\displaystyle -2 \bar {i} + 4 \bar {j} + 7 \bar {k} $$ and $$\displaystyle 3 \bar {i} - 5 \bar {j} + 8 \bar {k}$$ is
  • $$1 : 10$$
  • $$3 : 10$$
  • $$3 : 5$$
  • $$1 : 5$$
A point on the line $$\displaystyle \frac{x-1}{1}=\frac{y-2}{2}=\frac{z+1}{3}$$ at a distance$$\sqrt{6}$$ from the origin is 
  • $$\left (\displaystyle \frac{-5}{7},\frac{-10}{7},\frac{13}{7}\right)$$
  • $$(1,2,-1)$$
  • $$\left (\displaystyle \frac{5}{7},\frac{10}{7},\frac{-13}{7}\right)$$
  • $$(-1,-2,1)$$
A point $$Q$$ at a distance $$3$$ from the point $$P(1,1,1)$$ lying on the line joining the points $$A(0,-1,3)$$ and $$P$$, has the coordinates
  • $$(2,3,-1)$$
  • $$(4,7,-5)$$
  • $$(0,-1,3)$$
  • $$(-2,-5,7)$$
If two vertices of a triangle $$ABC$$ are $$A(-1,2,4)$$and $$B(2,-3,0)$$,and the centroid is $$(2,0,2)$$ then the vertex $$C$$ has the coordinates
  • $$(5,1,2)$$
  • $$\left ( 1,-\displaystyle \frac{1}{3},\frac{7}{3} \right )$$
  • $$\left ( 3,-\displaystyle \frac{2}{3},\frac{5}{3} \right )$$
  • none of these
Three vertices of a tetrahedron are $$(0,0,0),(6,-5,-1)$$and $$(-4,1,3)$$. If the centroid of the tetrahedron be$$(1,-2,5)$$ then the fourth vertex is
  • $$(2,-4,18)$$
  • $$(2,-4,-18)$$
  • $$\left (\displaystyle \frac{3}{4},\frac{-3}{2},\frac{7}{4} \right )$$
  • none of these
The points $$(4, -5, 1)$$, $$(3, -4, 0)$$, $$(6, -7, 3)$$, $$(7, -8, 4)$$ are vertices of a
  • square
  • parallelogram
  • rectangle
  • rhombus
Four vertices of a tetrahedron are $$(0,0,0),(4,0,0),(0,-8,0)$$ and $$(0,0,12)$$,Its centroid has the coordinates
  • $$\left ( \displaystyle \frac{4}{3},-\frac{8}{3},4 \right )$$
  • $$(2,-4,6)$$
  • $$(1,-2,3)$$
  • none of these
In geometry, we take a point, a line and a plane as undefined terms.
  • True
  • False
  • Ambiguous
  • Data Insufficient
A rectangular parallelopiped is formed by drawing planes through the points $$(-1,2,5)$$ and $$(1,-1,-1)$$ and parallel to the coordinate planes. the length of the diagonal of the parallelopiped is
  • $$2$$
  • $$3$$
  • $$6$$
  • $$7$$
The ratio of $$yz$$-plane divide the line joining the points $$A(3, 1,- 5), B(1, 4, -6)$$ is
  • $$3:1$$
  • $$-1:3$$
  • $$1:3$$
  • $$-3:1$$
0:0:1


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