Find the vector equation of a plane which is at a distance of `(6)/(sqrt29)` units from the origin and which is normal to `2 hati-3 hatj+ 4 hatk`. Convert it into cartesian from.

Find the equation of plane which is at a distance (4)/(sqrt(14)) from the origin and is normal to vector 2hati+hatj-3hatk .

Find the equation of plane which is at a distance 4/(sqrt(14)) from the origin and is normal to vector 2 hat i+ hat j-3 hat kdot

©answer any one question: (i) find the vector equation of the plane at a distance 6/(sqrt29) unit from the origin and perpendicular to the vector 2 hat i -3 hat j+ 4 hat k . Also convert this equation in cartesian form.

Find the vector equation of a plane which is at distance of 3 units from the origin and has 2,2,-1 as the direction ratios of a normal to it.Also find the position vector of the foot of the prependicular drown from the origin to it .

Find the equations to the straight lines which are at a distance of 2 unit from the origin and which pass throught the points (4,-2).

Find the points on the z-axis which are at a distance of sqrt(29) unit from the point ( 2, -3 , -2) .

Find the vector equation of the plane whose cartesian from of equation is 3x-4y+2z=5

Find the coordinates of the points on z-axis which are at a distance sqrt(29) unit from the point ( 2 , - 3 , - 1) .

Find the vector equation of a line which passes throught the point with position vector hati - 2hat j+4hatk and is in the direction of hati + 2hatj - hatk . Also reduce it to cartesian form.

Find the equation of the plane which passing through the point hati + hatj + hatk and parallel to the plane vec r.(2hati - hatj + 2hatk) = 0.