HSC Science (Electronics) 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

# Solution for Show that the lines  (x+1)/-3=(y-3)/2=(z+2)/1;  are coplanar. Find the equation of the plane containing them. - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

Login
Create free account

Forgot password?

#### Question

Show that the lines  (x+1)/-3=(y-3)/2=(z+2)/1;  are coplanar. Find the equation of the plane containing them.

#### Solution

Two lines

(x-x_1)/a_1=(y-y_1)/b_1=(z-z_1)/c_1 and (x-x_2)/a_2=(y-y_2)/b_2=(z-z_2)/c_2

are coplanar, if

|[x_2-x_1,y_2-y_1,z_2-z_1],[a_1,b_1,c_1],[a_2,b_2,c_2]|

Here,x1 = -1      y1 = 3      z1 = -2
x2 = 0       y2 = 7      z2 = -7
a1= -3       b1 = 2      c1 = 1
a2= 1        b2 = -3     c2 = 2

therefore |[0-(-1),7-3,-7-(-2)],[-3,2,1],[1,-3,2]|

=|[1,4,-5],[-3,2,1],[1,-3,2]|

=1(7)-4(-7)-5(7)

=0

The given lines are coplanar.
Equation of the plane, containing the given lines is

|[x_2-x_1,y_2-y_1,z_2-z_1],[a_1,b_1,c_1],[a_2,b_2,c_2]|=0

|[x-x_1,y-y_1,z-z_1],[-3,2,1],[1,-3,2]|=0

(x+1)(4+3)-(y-3)(-6-1)+(z+2)(9-2)=0

7x+7+7y-21+7z+14=0

7x+7y+7z=0

x+y+z=0

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (October) (with solutions)
Question 2.2.3 | 4.00 marks

#### Video TutorialsVIEW ALL [2]

Solution Show that the lines  (x+1)/-3=(y-3)/2=(z+2)/1;  are coplanar. Find the equation of the plane containing them. Concept: Coplanarity of Two Lines.
S