Find the equation of the plane passing through `(a ,b ,c)` and parallel to the plane ` vec rdot(hat i+ hat j+ hat k)=2.`

Find the vector equation of the Plane Passing through the intersection of the planes barr.(i+j+k)=6 and barr.(2i+3j+4k)=-5 and through the point (1,1,1).

The straight line r = (hat(i) + hat(j) + 2hat(k)) + t(2hat(i) + 5hat(j) + 3hat(k)) is parallel to the plane r.(2hat(i) + hat(j) - 3hat(k)) = 5 . Find distance between the straight line and plane

A plane is at a distance of 5 units from the origin and perpendicular to the vector 2hat(i) + hat(j) + 2hat(k) . The equation of the plane is a) vec(r ).(2hat(i) + hat(j) -2hat(k))=15 b) vec(r ).(2hat(i)+ hat(j)-hat(k))=15 c) vec(r ).(2hat(i) + hat(j)+ 2hat(k))=15 d) vec(r ).(hat(i) + hat(j) + 2hat(k))=15

If the projection of the vectors vec a on vec b is |vec a times vec b| and if 3 vec b= hat i+ hat j+ hat k then the angle between vec a and vec b is a) pi//3 b) pi//2 c) pi//4 d) pi//6

If the positions vectors of three consecutive vertices of a parallelogram are hat i+ hat j+ hat k, hat i+3 hat j+5 hat k and 7 hat i+9 hat j+11 hat k then the coordinates of the fourth vertex are a)(2,1,3) b)(6,7,8) c)(4,1,3) d)(7,7,7)

A body constrained to move along the Z-axis of a co-ordinate system is subjected to a constant force vec F=(hat i +2hat j + 3 hat k )N . What is the work done by this force in moving the body over a distance of 4m along z-axis ?

The distance between the line vec(r) = (2hat(i) + 2hat(j) - hat(k)) + lambda(2hat(i) + hat(j) - 2hat(k)) and the plane vec(r).(hat(i) + 2hat(j) + 2hat(k)) = 10 is equal to

Find a vector of magnitude 6 and perpendicular to both vec(a) = 2hat(i) + 2hat(j) + hat(k) and vec(b) = hat(i) - 2hat(j) + 2hat(k)

If the scalar product of the vector hat(i) + vec(j) + 2hat(k) with the unit vector along mhat(i) + 2hat(j) + 3hat(k) is equal to 2, then one of the values of m is