# Case study Chapter 11(Three dimension geometry)

A line through the points A(3, 4, 1) and B(5, 1, 6) is drawn.(Case study three dimension geometry 2 )

Based on the above information answer the following questions:

(i) Direction cosines of the line passing through the points A and B are

(a)

(b)

(c)

(d)

(ii) Direction ratios of the line passing through the points A and B are

(a) -2, -3, 5 (b) 2, 3, 5

(c) 2, -3, 5 (d) -2, -3, -5

(iii) Equation of the line passing through the points A and B in certain form is

(a)

(b)

(c)

(d)

(iv) The coordinates of the point where the line through the points A and B crosses the XY-plane is

(a)

(b)

(c)

(d)

(v) The coordinates of the point where the line through the points A and B crosses the XZ-plane is

(a)

(b)

(c)

(d)

Given points are A(3, 4, 1) and B(5, 1, 6)

∴ we have AB =

∴ Its direction ratio are  =

= 2 , -3, 5

Direction cosine are =

Given points are A(3, 4, 1) and B(5, 1, 6)

∴ Direction given by =

Equation of the line passing through the points are A(3, 4, 1) and B(5, 1, 6) in cartesian form  is given by

i.e.

Equation of the line passing through the points are A(3, 4, 1) and B(5, 1, 6) is

Since the line (i) croses the XY- plane

∴ The z co-ordinate of the point on the line (i) will be zero.

Putting z = 0 in (i), we get

∴ Co-ordinates of the points is

Equation of the line passing through the points are A(3, 4, 1) and B(5, 1, 6) is

Since the line (i) croses the XY- plane

∴ The y co-ordinate of the point on the line (i) will be zero.

Now, Putting z = 0 in (i), we get

∴ Co-ordinates of the points is

## Some other Case study

The equation of motion of a missile are x = 3t, y = -4t, z = t where the time ‘t’ is given in seconds, and the distance is measured in kilometres.(Case study three dimension geometry 1)

(i) What is the path of the missile ?

(a) Straight line       (b) Parabola

(c) Circle                   (d) Ellipse

(ii) Which of the following points lie on the path of the missile ?

(a) (6, 8, 2)               (b) (6, -8, -2)

(c) (6, -8, 2)             (d) (-6, -8, 2)

(iii) At what distance will the rocket be from the starting point (0, 0, 0) in 5 seconds ?

(a) √550 kms            (b) √650 kms

(c) √450 kms            (d) √750 kms

(iv) If the position of rocket at certain instant of time is (5, -8, 10), then what will be the height of the rocket from the ground ? ( The ground is considered as the xy – plane).

(a) 12 km                   (b) 11 km

(c) 20 km                  (d) 10 km

(v) For what value of k are the lines
and perpendicular ?

(a) 1                           (b) 2

(c) 3                           (d) None of these