CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Column I Column IIa. Lines x12=y+23=z1 and r=(3^i^j+^k)+t(^i+^j+^k) are p. intersectingb. Lines x+51=y37=z+33 and xy+2z4=0=2x+y3z+5=0 are q. perpendicularc. Lines (x=t3,y=2t+1,z=3t2) and r=(t+1)^i+(2t+3)^j+(t9)^k are r. paralleld. Lines r=(^i+3^j^k)+t(2^i^j^k) and r=(^i2^j+5^k)+s(^i2^j+34^k) are s. skew

Then which of the following is correct ?

A
aq,s; br; cp,q; dp
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
aq; br; cp,q; dp,q
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
as; br,s; cp; dp,q
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
aq,s; br,s; cp; dp
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A aq,s; br; cp,q; dp
a.
Line x12=y+23=z1 is along the vector a=2^i+3^j^k and line r=(3^i^j+^k)+t(^i+^j+^k) is along the vector b=^i+^j+^k.
Here ab.

Also, ∣ ∣311(2)10231111∣ ∣0

b.
The direction ratios of the line xy+2z4=0=2x+y3z+5=0 are ∣ ∣ ∣^i^j^k112213∣ ∣ ∣=^i+7^j+3^k.
Hence, the given two lines are parallel.

c.
The given lines are (x=t3,y=2t+1, z=3t2) and r=(t+1)^i+(2t+3)^j+(t9)^k,

x+31=y12=z+23
and x11=y32=z+91

The lines are perpendicular as (1)(1)+(2)(2)+(3)(1)=0.
Also, ∣ ∣31132(9)123121∣ ∣=0

Hence, the lines are intersecting.

d.
The given lines are r=(^i+3^j^k)+t(2^i^j^k) and r=(^i2^j+5^k)+s(^i2^j+34^k).
∣ ∣ ∣1(1)3(2)15211123/4∣ ∣ ∣=0

Hence, the lines are coplanar and intersecting (as the lines are not parallel).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Angle between Two Line Segments
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon