The position vectors of two given points P and Q are `8i+3j and 2i−5j` respectively, find the magnitude and direction of the vector PQ

The position vectors of two given points P and Q are 8hat i+3hat j and 2hat i-5hat j respectively; find the magnitude and direction of the vector (vec PQ)

If the position vectors of two given points A and B be 8vec i+3vec j+2vec k and 2vec i-5vec j+3vec k respectively,find the magnitude and direction of vec AB

If the position vectors of the points A and B are : 7hat(i)+3hat(j)-hat(k) and 2hat(i)-5hat(j)+4hat(k) respectively, find the magnitude and direction - cosines of the vector 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)

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 .

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.

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.

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