wiz-icon
MyQuestionIcon
MyQuestionIcon
14
You visited us 14 times! Enjoying our articles? Unlock Full Access!
Question

The lines xa+dαδ=yaα=zadα+δ and xb+cβr=ybβ=zbcβ+r are coplanar and then equation to the plane in which they lie, is?

A
x+y+z=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
xy+z=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x2y+z=0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
x+y2z=0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B x2y+z=0
The lines will be coplanar, if
∣ ∣adb+caba+dbcα+δαα+δβ+rββ+r∣ ∣=0
Add 3rd column to first and it becomes twice the second and hence the determinant is zero, as the two columns are identical. Again, the equation of the plane in which they lie is
∣ ∣xa+dyazadαδαα+δβrββ+r∣ ∣=0
On adding 1st and 3rd columns and subtracting twice the 2nd, we get
∣ ∣x+z2yyazad0αα+δ0ββ+r∣ ∣=0
[α(β+r)β(α+δ)](x+z2y)=0
(x+z2y)=0.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon