HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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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

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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

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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.
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