PQ , then m = n . And therefore, from Case I, the midpoint R of , will have its position vector as Example Consider two points P and Q with position vectors . Find the position vector of a point R which divides the line joining P and Q in the ratio : , (i) internally, and (ii) externally. Solution (i) The position vector of the point R dividing the join of P and Q internally in the ratio : is (ii) The position vector of the point R dividing the join of P and Q externally in the ratio : is Example Show that the points A( ), B( ), C( ) are the vertices of a right angled triangle.
Solution We have ( ) ( ) ( ) + −+ + −− = −− ( ) ( ) ( ) + −+ + −+ i ( ) ( ) ( ) + −+ = −+ Fig . Further, note that Hence, the triangle is a right angled triangle. EXERCISE . .
Compute the magnitude of the following vectors: = ˆ ; ; ˆ . Write two different vectors having same magnitude. . Write two different vectors having same direction.
. Find the values of x and y so that the vectors ˆ and xi yj are equal. . Find the scalar and vector components of the vector with initial point ( , ) and terminal point (– , ).
. Find the sum of the vectors = and = – . Find the unit vector in the direction of the vector = . Find the unit vector in the direction of vector , where P and Q are the points ( , , ) and ( , , ), respectively.
. For given vectors, = and = −+ , find the unit vector in the direction of the vector . Find a vector in the direction of vector which has magnitude units. .
Show that the vectors and are collinear. .