If the position vectors of A, B are i + j + k and i + j - 4k repectively then the position vector of the point which divides `bar(AB)` in the ratio 2 : 3 is

If the position vectors of A, B are 2i + 3j + k and 3i - j + 4k repectively then the position vector of the point which divides AB in the ratio 3 : 2 is

If the position vector of P,Q are I + j + k and I + 4j + 7k respectively then the position vector of the point which divides overline (PQ) in the ratio 2 : 1 is

If the position vectors of A and B are 3i - 2j + k and 2i + 4j - 3k then |vec(A)B|

If the position vectors of A, B are i + 2j - 3k, 3i - 2j + 5k respectively then the position vector of C in AB produced such that 2 AC = 3 AB is

If the position vectors of A and B are 3i - 2i + k and 2i + 4j - 3k then the length of AB is

The position vectors of A and B are 2hat i+hat j-hat k and hat i+2hat j+3hat k respectively. The position vector of the point which divides the line segment AB in the ratio 2:3 is

The position vectors of A and B are 2hat i+hat j-hat k and hat i+2hat j+3hat k respectively. The position vector of the point which divides the line segment AB in the ratio 2:3 is

If the position vectors of A, B are 2i - 9j - 4k, 6i - 3j + 8k then the unit vector in the direction of vec(A)B is

If A = i + 2j + 3k and B = 2i - j + 4k, then the position vectors of the points of trisection are