Fill in the blanks:
The equation of the line at a distance of 4 units from the origin and where the perpendicular from the origin makes an angle of `30^@` with +ve x-axis, is ……………….

A point on x - axis at a distance x from the origin .

A point on y axis at a distance y from the origin.

The distance of the pont P(4,3) from the origin is

Find the vector equations of the plane which is at a distance of 7 from the origin and its normal vector from the origin is 2hati-6hatj+3hatk .

Find the vector equation of a plane which is at a distance of 5 units from the origin and has as the direction numbers of a normal to the plane.

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3hati+5hatj-6hatk .

A line forms a triangle with co-ordinate axes. If the area of this triangle is 54 sqrt3 square units and the perpendicular drawn from the origin to the line makes an angle of 60^@ with the x-axis, find the equation of the line.

Find the vector equation of a plane, which is at a distance of 7 units from the origin and which is normal to the vector 3hati+5hatj-6hatk .

Find the vector equation of a plane, which is at a distance of 5 units from the origin and its normal vector is 2hati-3hatj+6hatk .

Find the distance of the line 4x - y = 0 from the point P (4, 1) measured along the line making an angle of 135^@ with the positive x-axis.