(Each question 1 marks)

Question 11 Mark

Find the distance between (2, -1, 3) and (-2, 1, 3) pairs of points.

Answer

Let A(2, -1, 3) and B(-2, 1, 3) be two points. Then
$AB = \sqrt {{{( - 2 - 2)}^2} + {{[1 - ( - 1)]}^2} + {{(3 - 3)}^2}}$ [using distance formula]
$= \sqrt {{{( - 2 - 2)}^2} + {{(1 + 1)}^2} + {{(3 - 3)}^2}}$
$= \sqrt {16 + 4 + 0} = \sqrt {20} = 2\sqrt 5$ units

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Question 21 Mark

Find the distance between (-1, 3, -4) and (1, -3, 4) pairs of points.

Answer

Let A(-1, 3, -4) and B(1, -3, 4) be two points. Then
$AB = \sqrt {{{[1 - ( - 1)]}^2} + {{( - 3 - 3)}^2} + {{[4 - ( - 4)]}^2}}$ [using distance formula]
$ = \sqrt {4 + 36 + 64} = \sqrt {104} = 2\sqrt {26}$

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Question 31 Mark

Find the distance between (-3, 7, 2) and (2, 4, -1) pairs of points.

Answer

Let A(-3, 7, 2) and B(2, 4, -1) be two points. Then
$AB = \sqrt {{{[2 - ( - 3)]}^2} + {{(4 - 7)}^2} + {{( - 1 - 2)}^2}}$ [using distance formula]
$= \sqrt {{{(2 + 3)}^2} + {{(4 - 7)}^2} + {{( - 1 - 2)}^2}}$$= \sqrt {25 + 9 + 9} = \sqrt {43}$ units

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Question 41 Mark

Find the distance between (2, 3, 5) and (4, 3, 1) pairs of points.

Answer

Let A(2, 3, 5) and B(4, 3, 1) be two points. Then
$AB = \sqrt {{{(4 - 2)}^2} + {{(3 - 3)}^2} + {{(1 - 5)}^2}} $ [using distance formula]

$= \sqrt {4 + 0 + 16} = \sqrt {20} = 2\sqrt 5$ units

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Question 51 Mark

Coordinate planes divide the space into ________ octants.

Answer

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Question 61 Mark

The coordinates of points in the XY-plane are of the form ________.

Answer

(x, y, 0).

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Question 71 Mark

The x-axis and y-axis taken together determine a plane known as ________.

Answer

XY-Plane

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Question 81 Mark

Name the octants in which the following points lie:
(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (-2, -4, -7)

Answer

Point (1, 2, 3) lies in Ist Octant.
Point (4, - 2, 3) lies in IVth Octant. Point (4, -2, -5) lies in VIIIth Octant.
Point (4, 2, -5) lies in Vth Octant. Point (-4, 2, -5) lies in VIth octant.
Point (-4, 2, 5) lies in IInd Octant. Point (-3, -1, 6) lies in IIIth octant.
Point (-2, -4, -7) lies in VIIth Octant.

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Question 91 Mark

A point is in the XZ-plane. What can you say about its y-coordinate?

Answer

Any point on the XZ-plane will have the coordinate (x, 0, z), so its y-coordinate is 0.

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Question 101 Mark

A point is on the X-axis. What are its y and z-coordinates?

Answer

Coordinates of any point on the X-axis is (x, 0, 0). So, its y and z-coordinates are zero.

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Question 111 Mark