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]