Home
Class 12
MATHS
If the straight lines x=1+s ,y=-3-lambda...

If the straight lines `x=1+s ,y=-3-lambdas ,z=1+lambdasa n dx=t/2,y=1+t ,z=2-t ,` with paramerters `sa n dt ,` respectivley, are coplanar, then find `lambdadot`

Text Solution

Verified by Experts

The given lines `(x+1)/(1)=(y-3)/(-lamda)=(z-1)/(lamda)=s`
`and " "(x-0)/(1//2)=(y-1)/(1)=(y-2)/(-1)=t`
are coplanar if `|{:(0+1,,1-3,,2-1),(1,,-lamda,,lamda),(1//2,,1,,-1):}|=0 or |{:(1,,-2,,1),(1,,-lamda,,lamda),(1//2,,1,,-1):}|=0`
or `" "1(lamda-lamda)+2(-1-(lamda)/(2))+1(1+(lamda)/(2))=0`
or `" "lamda=-2`
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

Angle between the straight lines (x-5)/7=(y+2)/-5=z/1 and x/1=y/2=z/3 is

The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n d(x-2)/1=(y-1)/(3)=(z+3)/2dot Statement 1: the given lines are coplanar. Statement 2: The equations 2r-s=1,r+3s=4a n d3r+2s=5 are consistent.

If the line (x-2)/(6) = (y-1)/(lambda) = (z+5)/(-4) is perpendicular to the straight line 3x - y - 2z = 7, then find the value of lambda

If the lines (x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1 intersect, then find the value of kdot

The angle between the straight lines x=5,y=4t+5,z=4t+3 and (x-5)/(5)=(y-6)/(0)=(z-(1)/(2))/(0) is-

If x prop y, y prop z, z prop t and t prop x where the constants of variation are k, l, m, n then

Prove that the stright line (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-3)/(4)=(z-4)/(5) are coplanar and find the equation of the plane in which they lie.

Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x^2-y^2+2y=1 is a. 2s qdotu n i t s b. 4s qdotu n i t s c. 6s qdotu n i t s d. 8s qdotu n i t s

Two lines L_(1): x = 5, (y)/(3-alpha) = (z)/(-2) and L_(2) : x = alpha, (y)/(-1) = (z)/(2- alpha) are coplanar. Then alpha can take value (s)

The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2+z^2-3x+3y+4z=8 is the same as the intersection of one of the spheres and the plane is a. x-y-z=1 b. x-2y-z=1 c. x-y-2z=1 d. 2x-y-z=1