Find the direction cosines of the unit vector perpendicular to the plane ` -> rdot(6 hat i-3 hat j-2 hat k)+1=0`passing through the origin.

Consider the Plane barr.(-6i-3j-2k)+1=0 . find the direction cosines perpendicular to the plane and perpendicular distance from the origin.

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

Find the Cartesian equation of the plane passing through the point (1,2,-3) perpendicular to the vector2i-j+2k .

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).

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)

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

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 a + b and a - b are perpendicular and b = 3hat(i) - 4hat(j) + 2hat(k) , then |a| is equal to