The x-intercept of plane which is passing through the intersection of planes `x+2y+3z+5=0` and `2x-3y+7z+1=0` and is parallel to the line `vec r=hat i+2 hat j+lambda(8 hat i-7 hat j-4 hat k)`, is (A) `13/5` (B) `-7/5` (C) `6/5` (D) `-9/5`

If the z -intercept of the plane which is passing through the intersection of the planes x+2y+3z+5=0 and 2x-5y+4z+7=0 and parallel to the line vec r=2hat i+5hat j+hat k+t(hat i+hat j+2hat k) is lambda then [|lambda|] equals (where t in R ) (where [.] denotes greatest integer function)

Let P=0 be the plane,passing through the line of intersection of the planes x+y+2z-4=0 & 2x-y-5z+1=0 & parallel to the vector (hat i+hat j+hat k) Then distance of P=0 from origin is

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r.( hat i- hat j+2 hat k)=5a n d vec r.(3 hat i+ hat j+ hat k)=6.

Find the equation of the plane passing through the intersection of the planes vec r .(2 hat i+ hat j+3 hat k)=7, vec r.(2 hat i+5 hat j+3 hat k)=9 the point (2,1,3)dot

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot (2 hat i-3 hat j+5 hat k) +7=0.

Find the equation of the plane which is parallel to the lines vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1"" and is passing through the point (0,1,-1 ).

Find the equation of the plane which is parallel to the lines vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1"" and is passing through the point (0,1,-1 ).