#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# The equation of plane through line of intersection of planes ax+by+cz+d=0 , a`x+b`y+c`z+d`=0 and parallel to line y=0,z=0 is??

Arun
25763 Points
3 years ago
Equation of any plane through the line of intersection of the given two planes
ax+ by+ cz+ d=0 and  a′x+ b′y+ c′z+ d′=0 is given by
(ax+by+cz+d) + λ(a′x+b′y+c′x+d′)=0

(a+λa′)x+(b+λb′)y+(c+λc′)z+(d+λd′)=0
But given that this plane is parallel to the line y=0,z=0y=0,z=0 (which is xaxis).
The normal n→=(a+λa′,b+λb′,c+λc′) is perpendicular to the line.( i.e., xaxis.)
(a+λa′,b+λb′,c+λc′).(1,0,0)=0
a+λa′=0orλ=−aa′
Substituting the value of λ we get the required eqn. of the plane is
(ab′−a′b)y+(bc′−b′c)z+(ac′−a′c)=0