A line passing through the point A(1,-1,-1) and is parallel to the vector `(3hat i-2hat j+3hat k)` .The shortest distance of the point (0,2,1) from the line is

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)

A line passes through the point A(5,-2.4) and it is parallel to the vector (2hat(i) -hat(j) +3hat(k)) .The vector equations of the line is

A line passes through the point (2,1,-3) and is parallel to the vector (hat(i) -2hat(j) +2hat(k)) . Find the equations of the line in vector and Cartesian forms .

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

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3hat i+2hat j-2hat k

A line passes through the point (3,4,5) and is parallel to the vector (2hat(i) +2hat(j) -3hat(k)) . Find the equations of the line in the vector as well as Cartesian forms.

Find the vector equation for the line which passes through the point (1, ,2 3) and parallel to the vector hat i-2 hat j+3 hat kdot reduce the corresponding equation in the Cartesian from.

(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 (2,1,-1) and parallel to the line vec r=(hat i+hat j)+lambda(2hat i-hat j+hat k)* Also,find the distance between these two lines.

A line passes through a point A with position voctor 3hat i+hat j-hat k and is parallel to the vector 2hat i-hat j+2hat k .If P is a point on this line such that AP=15 units,then the position vector of the point P is/are