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

Let A(a), B(b), C(c) and D(d) be four points such that a=2^i+4^j+3^k, b=2^i8^j, c=^i3^j+5^k, d=4^i+^j7^k. If m is the shortest distance between the lines AB and CD, then which of the following is (are) CORRECT?

A
m=0, hence AB and CD intersect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
m=[AB CD BD]AB×CD
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
AB and CD are skew lines and m=2313
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
m=[AB CD AC]AB×CD
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct options are
B m=[AB CD BD]AB×CD
C AB and CD are skew lines and m=2313
D m=[AB CD AC]AB×CD
Given, a=2^i+4^j+3^k ;b=2^i8^j c=^i3^j+5^k ;d=4^i+^j7^k AB=ba=4^i12^j3^k CD=dc=3^i+4^j12^k AC=ca=3^i7^j+2^k BD=db=2^i+9^j7^k

By definition,
m=(AB×CD)AC|AB×CD| (1)
=(AB×CD)BD|AB×CD| (2)

AB×CD=13(12^i+3^j+4^k) |AB×CD|=13144+9+16=169
m=13(12^i+3^j+4^k)169(3^i7^j+2^k) [ Using (1)]
=13169[3621+8]
=2313

Also, m=13(12^i+3^j+4^k)(2^i+9^j7^k)169 [ Using (2) ]
=13169[24+2728]
=2313

flag
Suggest Corrections
thumbs-up
7
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Application of Vectors - Lines
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon