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KC Sinha Mathematics Solution Class 11 Chapter 26 Introduction to Three-Dimensional Geometry Exercise 26.1

 Exercise 26.1

Page no 26.7

Question 1

Name the octants in which the following points lie: 
(i) (1,2,5)
(ii) (-3,-1,2)
(iii) (3,-1,2)
(iv) (1,2,-3)
(v) (-3,-1,2)
(vi) (-3,5,-2)
(vii) (-3,-1,2)
(viii) (-3,1,-2)
(ix) (-3,1,2)
(x) (-3,-1,6)
(xi) (1,2,3)
(xii) (-4,2,-5)

Question 2

Where are the following points :
(i) (0,0,-4)
(ii) (0,3,-2)

Question 3

A point lies in the X Z-plane. What can be said about its y-coordinate ?

Question 4

A point les on the x-axis. Find its y and z coordinates .

Question 5

Let P(2,4,5) be a point and F be the foot of perpendicular drawn from P to XZ-plane. Find the coordinates of F.

Question 6

Fill in the blanks :
(i) z-coordinate of a point lying in X Y-plane is
(ii) The x-axis and y-axis taken together determine a plane known as
(iii) The coordinates of points on x-axis are of the form
(iv) The coordinates of points in the X Y-plane are of the form
(v) Coordinates of points on YZ-plane is of the form
(vi) Coordinate planes divide the space into ... octants
(vii) Image of the point (1,2,3) in the X Y-plane is

Page no 26.8

Question 7

The coordinates of a point P are (1,2,3). Find the coordinates of the seven points such that the absolute values of their co-ordinates are the same as those of coordinates of P.

Question 8

The coordinates of a point are (1,-2,7). Write down the coordinates of seven points, whose absolute values are the same as those of the coordinates of the given point.

Question 9

Find the image of the point in the specified plane
(i) (0,0,-4) in X Y-plane
(ii) (-3,4,7) in the Y Z-plane
(iii) (5,4,-3) in the X Y-plane
(iv) (-7,2,-1) in the Z X-plane
(v) (-4,0,1) in the Z X-plane
(vi) (-2,0,0) in the X Y-plane

Question 10

Let A, B, C be the feet of perpendiculars drawn from a point P to x, y and z-axes respectively. Find the coordinates of A, B, C if coordinates of P are
(i) (4,-3,-7)
(ii) (3,4,2)(
(iii) (3,-5,1)
(iv) (4,-2,-6)

Question 11

Find the length of perpendiculars from point (1,-2,-5) to the coordinate planes.

Question 12

Find the distance of point (-1,-3,4) from x, y and z axes.

Question 13

Planes are drawn through points (1,-3,4) and (4,7,-2) parallel to coordinates planes. Find the lengths of the edges of the rectangular parallelopiped 50 formed.

Question 14

Planes are drawn parallel to the coordinate planes through the points (3,0,-1) and (-2,5,4). Find the lengths of the edges of the parallelopiped so formed.

Question 15

A rectangular parallelopiped is formed by drawing planes through the points (1,2,5) and (-1,-1,-1) parallel to the coordinate planes. Find the length of the diagonal of the parallelopiped.
[HOTS]
[Hint : Length of an edge of a rectangular parallelopiped is the distance between the parallel planes perpendicular to that edge]


































































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