The value of `(r.i)i+(r.j)j+(r.k)k` is

The value of (vec r*hat i)(vec r xxhat i)+(vec r*hat j)(vec r xxhat j)+(vec r*hat k)(vec r xxhat k) is equal to '

The value of (vec r*hat i)(vec r xxhat i)+(vec r*hat j)(vec r xxhat j)+(vec r*hat k)(vec r xxhat k) is equal to

For any vector vec r , the value of i xx (vec r xx i) + j xx (vec r xx j) + k xx (vec r xx k) =

If the vectors p hat(i)+hat(j)+hat(k), hat(i)+q hat(j)+hat(k) and hat(i)+hat(j)+r hat(k) (p ne q ne r ne 1) are coplanar, then the value of pqr -(p+q+r) is :

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

(r.i)(r xx i)+(r.j)(r xx xj)+(r.k)(r xx k) is equal to

(vec r . i) (vec r xx i) +(vec r .j) (vec r xx j)+ (vec r . k)(vec r xx k)=

The distance between the line vec r = 2i+2j+3k + lambda (i-j+4k) and the plane vec r . (i+5j+k) = 5 is