The position vector of a point p is ` r = x hati + y hatj + z hatk ` where ` x in N , ` y `in ` N and ` a = hati + hatj + hatk ` if r . `""` a = 10 then the number of possible position of P is

Find the position vector of the point where the line vec r = hati - hatj +hatk + t (hati + hatj -hatk ) meets the plane vecr. (hati + hatj + hatk ) =5

The component of vector vecA = a_x hati +a_y hatj + a_z hatk along the direction of 'hati - hatj'

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

If the points whose position vectors are 2hati + hatj + hatk , 6hati - hatj + 2 hatk and 14 hati - 5 hatj + p hatk are collinear, then p =

If the vectors p hati + hatj+ hatk, hati i+ q hatj + hatk and hati + hatj + r hatk ( p ne q ne r ne 1) are coplanar, then the value of pqr- (p + q + r) is :

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

If vec r = 3 hati + 2 hatj - 5 hatk , vec a= 2 hati - hatj + hatk, vec b = hati + 3 hatj - 2hatk and vec c=-2 hati + hatj - 3 hatk " such that " hat r = x vec a +y vec b + z vec c then

IF the vectors a = hati + hatj + hatk , b = hati - hatj + 2 hatk and c= x hati +(x-2) hatj - hatk are coplanar , then x=