Find the planes passing through the intersection of plane `rcdot(2hat(i)-3hat(j)+4hat(k))=1` and `rcdot(hat(i)-hat(j))+4=0` and perpendicular to planes `rcdot(2hat(i)-hat(j)+hat(k))=-8`

Find the equation of the plane through the line of intersection of : vec(r). (2 hat(i) - 3hat(j) + 4 hat(k) ) = 1 and vec(r). (hat(i) - hat(j) ) + 4 = 0 and perpendicular to the plane vec(r). (2 hat(i) - hat(j) + hat(k)) + 8 = 0 . hence, find whether the plane thus obtained contains the line: x - 1 = 2y - 4 = 3z - 12.

Find the unit vector perpendicular the plane rcdot(2hat(i)+hat(j)+2hat(k))=5 .

Find the equation of the plane through the line of intersection of vec r*(2hat i-3hat j+4hat k)=tandvec r*(hat i-hat j)+4=0 and perpendicular to vec r.(2hat i-hat j+hat k)+8=0

A unit vector in the plane of hat(i)+2hat(j)+hat(k) and hat(i)+hat(j)+2hat(k) and perpendicular to 2hat(i)+hat(j)+hat(k) , is

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

Find the distance between the planes r*(2hat(i)-hat(j)+3hat(k))=4andr*(6hat(i)-3hat(j)+9hat(k))+13=0

The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equidistant from the plane rcdot(5hat(i)+2hat(j)-7hat(k))+9=0 , then they are

Find the vector equation of a plane passing through the point having position vector 2 hat(i) + hat(j) + hat(k) and perpendicular to the vector : 4 hat(i) - 2 hat(j) + 3hat(k) .

Find the Cartesian equation of the plane, passing through the line of intersection of the planes: vec r*(2hat i+3hat j-4hat k)+5=0 and vec r*(hat i-5hat j+7hat k)+2=0 and intersecting y-axis at (0,3)

Find the equation of the plane passing through the line of intersection of the planes vec r*(hat i+hat j+hat k)=1 and vec r*(2hat i+3hat j-hat k)+4=0 and parallel to x-axis.