CBSE Questions for Class 11 Engineering Maths Introduction To Three Dimensional Geometry Quiz 7 - MCQExams.com

The planes $$2x - y + 4z = 5$$ and $$5x - 2.5y + 10z = 6$$ are
  • Parallel
  • Perpendicular
  • Intersect
  • intersect $$x$$ axis
The equation of plane passing through $$(-1,0,-1)$$ parallel to $$xz$$ plane is
  • $$y=-2$$
  • $$y=0$$
  • $$-x-z=0$$
  • None of the above
The distance of the point $$P(a, b, c)$$ from the $$x$$-axis is.
  • $$\sqrt{b^2+c^2}$$
  • $$\sqrt{a^2+c^2}$$
  • $$\sqrt{a^2+b^2}$$
  • $$a$$
If a line $$OP$$ of length $$r$$ (Where '$$O$$' is the origin) makes an angle $$\alpha$$ with x-axis and lies on the xz-plane, then what are the coordinates of $$P$$?
  • $$\left( r\cos { \alpha } ,0,r\sin { \alpha } \right) $$
  • $$\left( 0,0,r\sin { \alpha } \right) $$
  • $$\left( r\cos { \alpha } ,0,0 \right) $$
  • $$\left( 0,0,r\cos { \alpha } \right) $$
Which of the following is true for a plane?
  • A locus is called a plane if the line joining any two arbitrary points on the locus is also a part of the locus.
  • Value of $$y$$ in a $$zx$$ plane is non-zero.
  • Value of $$z$$ in a $$xy$$ plane is zero.
  • None of the above
Points $$A(3,2,4),B\left( \cfrac { 33 }{ 5 } ,\cfrac { 28 }{ 5 } ,\cfrac { 38 }{ 5 }  \right) $$, and $$C(9,8,10)$$ are given. The ratio in which $$B$$ divides $$\overline { AC } $$ is
  • $$5:3$$
  • $$2:1$$
  • $$1:3$$
  • $$3:2$$
The locus of a point, which is equidistant from the points $$(1, 1)$$ and $$(3, 3)$$, is
  • $$y = x + 4$$
  • $$x + y = 4$$
  • $$x = 2$$
  • $$y = 2$$
  • $$y = -x$$
Let $$O$$ be the origin and $$A$$ be the point $$(64, 0)$$. If $$P$$ and $$Q$$ divide $$OA$$ in the ratio $$1 : 2 : 3$$, then the point $$P$$ is
  • $$\left (\dfrac {32}{3}, 0\right )$$
  • $$(32, 0)$$
  • $$\left (\dfrac {64}{3}, 0\right )$$
  • $$(16, 0)$$
  • $$\left (\dfrac {16}{3}, 0\right )$$
The shortest distance between z-axis and the line 
$$x+y+2z-3=0=2x+3y+4z-4$$, is _____________
  • $$1$$
  • $$2$$
  • $$4$$
  • $$3$$
If $$z_{1}$$ and $$z_{2}$$ are $$z$$ co-ordinates of the points of trisection of the segment joining the points $$A(2, 1, 4), B(-1, 3, 6)$$ then $$z_{1} + z_{2} =$$
  • $$1$$
  • $$4$$
  • $$5$$
  • $$10$$
In the triangle with vertices $$A(1, -1, 2), B(5, -6, 2)$$ and $$C(1,3,-1)$$ find the altitude $$n=|BD|$$.
  • $$5$$
  • $$10$$
  • $$5\sqrt{2}$$
  • $$\displaystyle\frac{10}{\sqrt{2}}$$
The distance between the X-axis and the point $$(3, 12, 5)$$ is
  • 3
  • 13
  • 14
  • 12
  • 5
The point which divides the line joining the points $$ (1, 3, 4)$$ and $$(4,3,1)$$ internally in the ratio $$ 2:1 , $$ is 
  • $$ (2, -3, 3 ) $$
  • $$ (2, 3, 3) $$
  • $$ \left( \dfrac {5}{2} , 3 , \dfrac {5}{2} \right) $$
  • $$ ( -3, 3, 2 ) $$
  • $$ ( 3,3,2) $$
The coordinates of the foot of the perpendicular drawn from the point $$A(1,0,3)$$ to the join of the points $$B(4,7,1)$$ and $$C(3,5,3)$$ are
  • $$(5,7,17)$$
  • $$\left( \cfrac { -5 }{ 7 } ,\cfrac { 7 }{ 3 } ,\cfrac { -17 }{ 3 } \right) $$
  • $$\left( \cfrac { 5 }{ 7 } ,\cfrac { -7 }{ 3 } ,\cfrac { 17 }{ 3 } \right) $$
  • $$\left( \cfrac { 5 }{ 7 } ,\cfrac { 7 }{ 3 } ,\cfrac { 17 }{ 3 } \right) $$
If xy -plane and yz-plane divides the line segment joining A(2,4,5) and B(3,5,-4) in the ratio a:b and p:q respectively then value of $$\left( {{a \over b},{p \over q}} \right)$$  may be
  • $${\dfrac{23}{12}}$$
  • $${\dfrac{7}{5}}$$
  • $${\dfrac{7}{12}}$$
  • $${\dfrac{21}{10}}$$
A swimmer can swim $$2$$ km in $$15$$ minutes in a lake and in a river he can swim a distance of $$4$$ km in $$20$$ minutes along the stream. If a paper boat is put in the river, then the distance covered by it in $$\displaystyle $$2$$ \, \frac{1}{2}$$2 hours will be 
  • $$18$$ km
  • $$12$$ km
  • $$8$$ km
  • $$10$$ km
In a $$\triangle {ABC}$$, side $$AB$$ has the equation $$2x+3y=29$$ and the side $$AC$$ has the equation $$x+2y=16$$. If the mid point of $$BC$$ is $$(5,6)$$, then the equation of $$BC$$ is
  • $$2x+y=7$$
  • $$x+y=1$$
  • $$2x-y=17$$
  • None of these
Plane $$ax + by + cz = 1$$ intersect axes in $$A, B, C$$ respectively. If $$G\left (\dfrac {1}{6}, -\dfrac {1}{3}, 1\right )$$ is a centroid of $$\triangle ABC$$ then $$a + b + 3c =$$ _________.
  • $$\dfrac {4}{3}$$
  • $$4$$
  • $$2$$
  • $$\dfrac {5}{6}$$
If $$xy-$$plane and $$yz-$$plane divides the line segment joining $$A(2,4,5)$$ and $$B(3,5,-4)$$ in the ratio $$a:b$$ and $$p:q$$ respectively then value of $$\left(\dfrac {a}{b}+\dfrac {p}{q}\right)$$ may be
  • $$\dfrac {23}{12}$$
  • $$\dfrac {7}{5}$$
  • $$\dfrac {7}{12}$$
  • $$\dfrac {21}{10}$$
Locus of a point $$P$$ which such that $$PA = PB$$ where $$A = (0, 3, 2)$$ and $$B = (2, 4, 1)$$ is
  • $$2x + y - z = 4$$
  • $$x - 2y + z + 1 = 0$$
  • $$9x - 2y + 4z - 5 = 0$$
  • None of these
Points $$(5, 0, 2), (2, -6, 0), (4, -9, 6)$$ & $$(7, -3, 8)$$ are vertices of a 
  • Square
  • Rhombus
  • Rectangle
  • Parallelogram
The values of a for which $$(8,-7,a),(5,2,4)$$ and $$(6,-1,2)$$ are collinear , is given by 
  • $$2$$
  • $$-2$$
  • $$-1$$
  • $$1$$
Given $$A(3, 2, -4), B(5, 4, -6)$$ & $$C(9, 8, -10)$$ are collinear. Ratio in which $$B$$ divides $$AC$$
  • $$1:2$$
  • $$2:1$$
  • $$-1:2$$
  • None of these
A cube of side 5 has one vertex at the point (1,0,-1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive  z-axis. Find the coordinates of the other vertices of the cube.
  •  (1,0,1)
  •  (0,-1,0)
  •  (0,0,-1)
  • (1,0,0)
If $$O=(0,0,0),OP=5$$ and the d.rs of OP are $$1,2,2$$ then $$P_x+P_y+P_z=$$
  • $$25$$
  • $$\dfrac{25}{9}$$
  • $$\dfrac{25}{3}$$
  • $$\left(\dfrac{5}{3},\dfrac{10}{3},\dfrac{10}{3}\right)$$
Find the co-ordinates of a point lying on the line $$\dfrac{x -2}{3} = \dfrac{y + 3}{4} = \dfrac{z - 1}{7}$$ which is at a distance $$10$$ units from $$(2, -3, 1)$$.
  • $$(32,37,71)$$
  • $$(-28,-43,-69)$$
  • $$(-32,-37,-71)$$
  • None of these
The ratio in which the join of $$(1, -2, 4)$$ and $$(4, 2, -1)$$ divided by the $$XY$$ plane is
  • $$1:3$$
  • $$3:1$$
  • $$4:1$$
  • $$1:4$$
A plane meets the co-ordinate axes in A,B,C such that the centroid of the triangle ABC is the point $$(p,q,r)$$. The equation of the plane is 
  • $$\dfrac{x}{p} + \dfrac{y}{q} + \dfrac{z}{r} = 0$$
  • $$\dfrac{x}{p} + \dfrac{y}{q} + \dfrac{z}{r} = 1$$
  • $$\dfrac{x}{p} + \dfrac{y}{q} + \dfrac{z}{r} = 2$$
  • none of these
If a point $$P$$ from where line drawn cuts coordinates axes at $$A$$ and $$B$$ (with $$A$$ on $$x-$$axis and $$B$$ on $$y-$$axis ) satisfies $$\alpha \dfrac{x^{2}}{PB^{2}}+\beta \dfrac{y^{2}}{PA^{2}}=1$$, then $$\alpha+\beta$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
The distance between the points $$(\cos \theta, \sin \theta)$$ and $$(\sin \theta - \cos \theta)$$ is
  • $$\sqrt {3}$$
  • $$\sqrt {2}$$
  • $$2$$
  • $$1$$
0:0:1


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