Question

The direction ratios of the line of intersection of the
planes x + 2y + z = 3 and 6x + 8y + 3z = 13 are
A. < -2,3, -4>
< 2,1,4 >
© <-3,2,4 >
0
< 4,3,2 >​

Answer 1

The equation of the line of intersection of the planes x+2y+z=3 and 6x+8y+3z=13 can be written as

x−2/2 = y+1/−3 = z−3/4

x−2/2 = y+1/3 = z−3/4

x+2/2 = y−1/−3 = z−3/4

x+2/2 = y+2/3 = z−3/4

Answer :

A

explaination :

Let the Dr's of a required line a,b and c. Since, the normal to the given planes x+2y+z=3and6x+8y+3z=13 are perpendicular to the line

∴a+2b+c=0 [∵a1a2+b1b2+c1c2=0]

and 6a+8b+3c=0

⇒ a/6−8 = b/6−3 = c/8−12

⇒ a/−2 = b/3 = c/−4

or a/2 = b/−3= c/4

Also, line passes through (2,-1,3).

∴ Equation is x−2/2 = y+1/−3= z−3/4

JAI SHREE KRISHNA