A plane `P` passes through the point `(1,1,1)` and is parallel to the vectors `vec a=-hat i+hat j` and `vec b=hat i-hat k`. The distance of the point `((3sqrt(3))/(2),3sqrt(3),3)` from the plane is equal to

Vectors vec A=hat i+hat j-2hat k and vec B=3hat i+3hat j-6hat k are

A line passes through the point A(hat i+2hat j+3hat k) and is parallel to the vector vec V=(hat i+hat j-hat k) The shortest distance from the origin,of the line is (A) sqrt(2)(B)sqrt(4)(C)sqrt(5) (D) sqrt(6)

Find the equation of the plane passing through the point A=(3,-2,-1) and perpendicular to the vactors vec b=hat i-2hat j-4hat k,vec c=3hat i+2hat j-5hat k

Write the vector equation of the plane passing through the point (a,b,c) and parallel to the plane vec r.(hat i+hat j+hat k)=2

Find the point where line which passes through point (1,2,3) and is parallel to line vec r=hat i+hat j+2hat k+lambda(hat i-2hat j+3hat k) meets the xy-plane.

Write the vector equation of the plane,passing through the point (a,b,c) and parallel to the plane vec r*(hat i+hat j+hat k)=2

Find the vector equation of the line passing through the point (1,2) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6

Find a unit vector parallel to the resultant of vectors vec A = 3 hat I + 3 hat j - 2 hat k and vec B= hat i- 5 hat j + hat k .

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec r*(hat i-hat j+2hat k)=5 and vec r*(3hat i+hat j+hat k)=6