The angle between `(hat i+hat j+hat k)` and line of the intersection of the plane `2x+y+4z=0` and `3x+4y+z=0` is

Angle between hat i+hat j and the line of intersection of the planes vec r*(hat i+2hat j+3hat k)=0 and vec r*(3hat i+3hat j+hat k)=0 is equal to

Find the equation of the plane through the point 2 hat i+ hat j- hat k and passing through the line of intersection of the plane vec rdot(( hat i+3 hat j- hat k)=0\ a n d\ vec rdot(( hat j+2 hat k)=0.

(i) Find the vector equation of the plane through the intersection of the planes : vec(r) . (hati + hatj + hatk) = 6, vec(r) . (2 hati + 3 hatj + 4 hatk) = -5 and the point (1,1,1). (ii) Find the equation of the plane which contains the line of intersection of the planes : vec(r) . (hat(i) + 2 hat(j) + 3 hat(k) ) - 4 = 0. vec(r). (2 hat(i) + hatj - hat(k) ) + 5 = 0 and which is perpendicular to the plane : vec(r) . (5 hati + 3 hatj - 6 hatk ) + 8 = 0 . (iii) Find the equation the plane passing through the intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1,1,1) .

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)

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

Find the equation of the plane through the pooint (4,-3,2) and perpendicular to the line of intersection of the planes x-y+2z-3=0 and 2z-y-3z=0 FInd the point of the intersection of the line vec r=hat i+2hat j-hat k+lambda(hat i+3hat j-9hat k) and the plane obtained above

The vector equation of the plane through the point hat(i)+2hat(j)-hat(k) and perpendicular to the line of intersection of the plane rcdot(3hat(i)-hat(j)+hat(k))=1 and rcdot(hat(i)+4hat(j)-2hat(k))=2 , is

The line vec r=2hat i-2hat j+5hat k+lambda(hat i-3hat j+2hat k) intersects the plane 2x-3y+4z=163 at P and intersects the YZ plane at Q. If the distance PQ is 9sqrt(a) where a in N then a equals

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 distance between the point with position vector -hat i-5hat j-10hat k and the point of intersection of the line (x-2)/(3)=(y+1)/(4)=(z-2)/(12) with the plane x-y+z=5