Home
Class 12
MATHS
If the lines (x-1)/2=(y+1)/3=(z-1)/4 and...

If the lines `(x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1` intersect then the value of k is (A) `3/2` (B) `9/2` (C) `-2/9` (D) `-3/2`

A

`3//2`

B

`9//2`

C

`-2//9`

D

`-3//2`

Text Solution

Verified by Experts

The correct Answer is:
b
`(x-1)/(2)= (y+1)/(3)= (z-1)/(4)=lamda`
`rArr" "x=2lamda+1, y=3lamda-1 and z=4lamda+1`
`" "(x-3)/(1)= (y-k)/(2)= (z)/(1)= mu`
`rArr" "x=3+mu, y=k+2mu and z=mu `
Since the above lines intersect,
`" "2lamda+1= 3+mu" " `(i)
`" "3lamda-1= 2mu +k" "` (ii)
`" "mu = 4lamda +1" "` (iii)
Solving (i) and (iii) and putting the value of `lamda and mu` in (ii), `k = 9//2`.
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES MULTIPLE CORRECT ANSWERS TYPE|4 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES REASONING TYPE|2 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES SUBJECTIVE TYPE|5 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

If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersect, then find the value of k .

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

If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersect, then k is equal to (1) -1 (2) 2/9 (3) 9/2 (4) 0

If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersect, then k is equal to (1) -1 (2) 2/9 (3) 9/2 (4) 0

If the line (x-1)/(2)=(y+1)/(3)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/(1) intersect, then k is equal to

The lines (x-1)/1=(y-2)/2=(z-3)/(3) and (x-1)/1=y/3 =z/4 are

If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)/(2)=(z-5)/(1) intersect then

The line (x-2)/1=(y+4)/(2)=(z-3)/3 and x/2=(y-1)/(4)=(z+3)/(6) are

The projection of the line (x-1)/(2)=(y+1)/(2)=(z-1)/(4) and (x-3)/(1)=(y-k)/(2)=(z)/(1) , intersect , then k is equal to

If the straight lines (x-1)/k=(y-2)/2=(z-3)/3 and (x-2)/3=(y-3)/k=(z-1)/2 intersect at a point, then the integer k is equal to (1) -5 (2) 5 (3) 2 (4) -2