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MATHS Fill In The Blanks[1 Marks ]

Introduction to Three Dimensional Geometry · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 18 questions.

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Fill In The Blanks[1 Marks ]

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18 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
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If the mid-points of the sides of a triangle AB; BC; CA are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4), then the centriod of the triangle ABC is ________.
Answer
If the mid-points of the sides of a triangle AB; BC; CA are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4), then the centriod of the triangle ABC is (1, 1, -2).Solution:
Given that, mid-points of sides of AABC are D(1, 2, -3), E(3, 0, 1) and F(-1, 1, -4). Now, from the geometry of centroid, we know that the centroid of $\triangle\text{DEF}$ is same as the centroid of $\triangle\text{ABC}.$ $\therefore$ Centroid of $\triangle\text{ABC}\equiv\text{G}\Big(\frac{1+3-1}{3},\frac{2+0+1}{3},\frac{"-3+1-4}{3}\Big)\equiv\text{G}(1,1,-2)$
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Question 21 Mark
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A line is parallel to x-axis if all the points on the line have equal ________.
Answer
A line is parallel to x-axis if all the points on the line have equal y and z coordinates. Solution:Hence, the value of the filler is y and z coordinates.
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Question 31 Mark
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The coordinates of a point are the perpendicular distance from the ________ on the respectives axes.
Answer
The coordinates of a point are the perpendicular distance from the given points on the respectives axes.
Solution:
Hence, the value of the filler is given points.
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Question 41 Mark
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Coordinate planes divide the space into ______ octants.
Answer
Coordinate planes divide the space into eight octants.
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Question 51 Mark
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The coordinates of points in the XY-plane are of the form _______.
Answer
The coordinates of points in the XY-plane are of the form (x, y, 0).
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Question 61 Mark
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The equation of z-axis, are _______.
Answer
The equation of z-axis, are x = 0, y = 0.
Solution:
Any point on the z-axis is taken as (0, 0, z).
So, for any point on z-axis, we have x = 0 and y = 0, which together represents its equation.
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Question 71 Mark
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A line is parallel to xy-plane if all the points on the line have equal ________.
Answer
A line is parallel to xy-plane if all the points on the line have equal z-coordinate.
Solution:
A line is parallel to xy-plane if each point P(x, y, z) on it is at same distance from xy-plane.
Distance of point P from xy plane is ‘z’
So, line is parallel to xy-plane if all the points on the line have equal z-coordinate.
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Question 81 Mark
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The three axes OX, OY, OZ determine ________.
Answer
The three axes OX, OY, OZ determine three coordinate planes.
Solution:
Hence, the filler value is three coordinate planes.
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Question 91 Mark
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If the distance between the points (a, 2, 1) and (1, -1, 1) is 5, then a _______.
Answer
If the distance between the points (a, 2, 1) and (1, -1, 1) is 5, then a = 5 or -3.Solution:
Given points are (a, 2, 1) and (1, -1, 1). $\therefore\sqrt{(\text{a}-1)^2+(2+1)^2+(1-1)^2}=5$ (Given) $\Rightarrow(\text{a}-1)^2+9+0=25$ $\Rightarrow\text{a}^2-2\text{a}-15=0$ $\Rightarrow(\text{a}-5)(\text{a}+3)=0$ $\therefore\text{a}=5\ \text{or}\ -3$
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Question 101 Mark
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The three planes determine a rectangular parallelopiped which has ________ of rectangular faces.
Answer
The three planes determine a rectangular parallelopiped which has three planes of rectangular faces. Solution: As shown in the figure rectangular parallelepiped is determined by three planes ABB' A', AA' D'D, A'B'C'D'. In this parallelepiped we have three pairs of rectangular faces, viz., (ABB'A', DCC'D'), (ABCD, A'B'C'D'), (ADD'A', BCC'B')
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Question 111 Mark
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The three coordinate planes divide the space into ________ parts.
Answer
The three coordinate planes divide the space into Eight parts.
Solution:
Hence, the values of the filler is eight.
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Question 121 Mark
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The x-axis and y-axis taken together determine a plane known as_______.
Answer
The x-axis and y-axis taken together determine a plane known as XY -plane.
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Question 131 Mark
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The equation of yz-plane is ________.
Answer
The equation of yz-plane is x = 0.
Solution:
On yz-plane for any point x-coordinate is zero.
So, yz-plane is locus of point such that x = 0, which is its equation.
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Question 141 Mark
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The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are ______.
Answer
The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are $\sqrt{333}$.Solution:
The given dimensions are 10, 13 and 8 $\therefore$ Reuired lenghth $=\sqrt{\text{a}^2+\text{b}^2+\text{c}^2}$ $=\sqrt{(10)^2+(13)^2+(8)^2}$ $=\sqrt{100+169+64}=\sqrt{333}$ Hence, the value of the filler is $\sqrt{333}.$
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Question 151 Mark
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x = a represent a plane parallel to ________.
Answer
x = a represent a plane parallel to yz-plane.
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Question 161 Mark
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The plane parallel to yz-plane is perpendicular to ________.
Answer
The plane parallel to yz-plane is perpendicular to x-axis.Solution:
Hence, the value of the filler is x-axis.
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Question 171 Mark
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If a point P lies in yz-plane, then the coordinates of a point on yz-plane is of the form ________.
Answer
If a point P lies in yz-plane, then the coordinates of a point on yz-plane is of the form (0, y, z).
Solution:
We know that, on yz-plane, x = 0.
So, the coordinates of the required point are (0, y, z).
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Question 181 Mark
Fill in the blanks.
If the point P lies on z-axis, then coordinates of P are of the form ________.
Answer
If the point P lies on z-axis, then coordinates of P are of the form (0, 0, z).
Solution:
On the z-axis, x = 0 and y = 0.
So, the required coordinates are of the form (0, 0, z).
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