wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The shortest distance between the lines xy=0=2x+z and x+y2=0=3xy+z1 is

A
111
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
123
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is D 111
L1:xy=0=2x+z and
L2:x+y2=0=3xy+z1
It can also be write as
L1:x1=y1=z2
L2:x1=y21=z34

A(0,0,0) be the point on L1 and B=(^i+^j2^k) is a direction of L1
C(0,2,3) be the point on L2 and D=(^i+^j+4^k) is a direction of L2
B×D=6^i2^j+2^k

B×D=62+22+22=211

CA=2^j+3^k

(B×D).(CA)=(6^i2^j+2^k)(2^j+3^k)=2

The shortest distance between line L1 and L2 can bee found using the following formula.
Distance =∣ ∣B×D|B×D|.(CA)∣ ∣
Distance =111

Hence, option A.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Shortest Distance between Two Skew Lines
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon