A man walks a distance of 3 units from the origin towards the north east (`N45^@E)` direction.from there he walks a distance of 4 units towards the north west `(N45^@W)` direction of reach a point P then the position of P in the Argand plane is :

(xvi) The distance of a point from the x-axis is 7 units on the negative directions and the distance from the y-axis is 8 units on the positive direction. Find the co-ordinates or the point.

A point charge +q is placed at a distance a from an isolated conducting surface. The field at a point P on the other side of the plane is directed

A person walks 2sqrt(2) units away from origin in south west direction (S45^(@)W) to reach A , then walks sqrt(2) units in south east direction (S45^(@)E) to reach B . From B he travel is 4 units horizontally towards east to reach C . Then he travels along a circular path with centre at origin through an angle of 2pi//3 in anti-clockwise direction to reach his destination D . Position of D in argand plane is ( w is an imaginary cube root of unity)

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 unit vector in the direction of the vector whose initial point is P(4,5) and terminal point is Q(-2, 13)

If P(x, y, z) is a point in the space at a distance r from the origin O, then the direction cosines of the line OP are-

Find the equations to the straight lines which are at a distance of 2 unit from the origin and which pass through the point of intersection of the lines 3x+4y=4 and 2x+5y+2=0 .

A circle of radius 5 units has diameter along the angle bisector of the lines x+y=2 and x-y=2. If the chord of contact from the origin makes an angle of 45^0 with the positive direction of the x-axis, find the equation of the circle.

The point (4,1) undergoes the following three transformations successively (a) Reflection about the line y=x (b)Translation through a distance 2 units along the positive direction of the x-axis ( c) Rotation through an angle pi//4 about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates

Equation of the straight line meeting the cirle with centre at origin and radius equal to 5 in two points at equal distances of 3 units from the point (3,4) is