If `veca = 4hat i-3hat j and vec b =-2hat i+ 5hat j` are the position vectors of the points A and B respectively ;find (i) the position vector of the middle point of the `bar(AB)`

If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the position vectors of the points A and B respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vectors of the points of trisection of the line-segment bar(AB) .

If vec a=4hat i-3hat j and vec b=-2hat i+5hat j are the position vectors of the points A and B respectively; find the points A and B middle point of the line-segment vec AB; (ii) the position vectors of the points of trisection of the line-segment vec AB

The position vectors of the points A and B are 3hat i-hat j+7hat k and 4hat i-3hat j-hat k; find the magnitude and direction cosines of bar(AB)

If hat i+hat j+hat k,2hat i+5hat j,3hat i+2hat j-3hat k and hat i-6hat j-hat k are the position vectors of points A,B,C and D respectively,then find the angle between vec AB and vec CD. Deduce that vec AB and vec CD

The position vectors of the points A and B are respectively 3hat(i)-5hat(5) + 2 hat(k) and hat(i)+hat(j)-hat(k) . What is the length of AB ?

The position vecors of the points A and B are 4hat(i)-3hat(j)+5hat(k) " and " -2hat(i)+3hat(j)+2hat(k) respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vector of the points of trisection of the line-segment bar(AB) .

The position vectors of the points A and B are 3hat i-hat j+7hat k and 4hat i-3hat j-hat k; find the magnitude and direction cosines of vec AB .

If vec(a)=-2hat(i)+3hat(j)+5hat(k), vec(b)=hat(i)+2hat(j)+3hat(k) and vec(c )=7 hat(i)-hat(k) are position vectors of three points A, B, C respectively, prove that A, B, C are collinear.

vec [AB]=3hat i+ hat j+ hat k and vec [CD]= -3hat i+2 hat j+4 hat k are two vectors. The position vectors of points A and C are 6 hat i+ 7 hat j+ 4 hat k and -9 hat j +2 hat k respectively. Find the position vector of point P on the line AB and point Q on the line CD such that vec [PQ] is perpendicular to vec [AB] and vec [CD] both.