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 `(vecPQ)`

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 8hat(i)+3hat(j)+2hat(k) " and " 2hat(i)-5hat(j)+3hat(k) respectively, find the magnitude and direction of 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 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 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 vec(AB)

If the position vectors of the points P and Q are 2hat(i)+hat(k) " and " -3hat(i)-4hat(j)-5hat(k) respectively, then vector vec(OP) is -

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.

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

The position vectors of the points P and Q are 5 hat i+7 hat j- 2 hat k and -3 hat i+3 hat j+6 hat k respecively. The vector vec A=3 hat i-hat j+hat k passes through the point P and the vector vec B=-3 hat i+2 hat j+4 hat k passes through the point Q. A third vector 2 hat i+7 hat j- 5hat k intersects vectors vec A and vec B . Find the position vectors of the points of intersection