Home
Class 12
MATHS
Consider the lines L(1): (x-1)/(2)=(y)/(...

Consider the lines `L_(1): (x-1)/(2)=(y)/(-1)= (z+3)/(1) , L_(2): (x-4)/(1)= (y+3)/(1)= (z+3)/(2) ` and the planes `P_(1)= 7x+y+2z=3, P_(2): 3x+5y-6z=4`. Let `ax+by+cz=d` be the equation of the plane passing through the point of intersection of lines `L_(1) and L_(2)`, and perpendicular to planes `P_(1) and P_(2)`.
Match Column I with Column II.

Text Solution

Verified by Experts

The correct Answer is:
` a to r; b to q; c to s; d to p`
Plane perependicular to `P_(1) and P_(2)` has direction ratios of normal
`" "|{:(hati,,hatj,,hatk),(7,,1,,2),(3,,5,,-6):}|= -16hati+48hatj+32hatk" "` (i)
For point of intersection of lines
`" "(2lamda_(1)+1, -lamda_(1), lamda_(1)-3)-=(lamda_(2)+4, lamda_(2)-3, 2lamda_(2)-3)`
`rArr" "2lamda_(1)+1= lamda_(2)+ 4 or 2 lamda_(1)-lamda_(2)=3`
and `" "-lamda_(1)= lamda_(2)-3 or lamda_(1)+lamda_(2)=3`
`rArr" "lamda_(1)=2, lamda_(2)=1`
`therefore" "` Point is `(5, -2, -1)" "`(ii)
From (i) and (ii), required planes is
`" "-1(x-5)+ 3(y+2)+ 2(zk+1)=0`
or `" "x -3y-2z=13`
`rArr " "a=1, b=-3, c=-2, d=13`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES LINKED COMPREHENSION TYPE|3 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

Consider the line L_(1) : (x-1)/(2)=(y)/(-1)=(z+3)/(1), L_(2) : (x-4)/(1)=(y+3)/(1)=(z+3)/(2) find the angle between them.

Consider the lines L_1:(x-1)/2=y/(-1)=(z+3)/1,L_2:(x-4)/1=(y+3)/1=(z+3)/2 and the planes P_1:7x+y+2z=3,P_2:3x+5y-6z=4. Let a x+b y+c z=d be the equation of the plane passing through the point match Column I with Column II. Column I, Column II a= , p. 13 b= , q. -3 c= , r. 1 d= , s. -2

L_(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L_(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) The lines L_(1) and L_(2) are -

Find the equation of the plane passing through the line of intersection of the planes 4x-5y-4z=1 and 2x+y+2z=8 and the point (2,1,3).

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7 is

Find the equation of the plane passing through the point (-1,-1,2)a n d perpendicular to the planes 3x+2y-3z=1 a n d5x-4y+z=5.

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7

The equation of the plane passing through the line of intersection of the planes x+y+z+3 =0 and 2x-y + 3z +2 =0 and parallel to the line (x)/(1) = (y)/(2) = (z)/(3) is

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5, which is perpendicular to the plane x - y + z = 0.