If a point C divides the line segment joining the points with the position vectors 2 i -3 j +2 k and 3 i - j -2 k in the ratio 2: 3 , then the distance of C from the point with position vector 2 i - j + k is

Step-by-step solution

Let r is the position vector of the point C . Since, point C divides the line segment joining the points with the position vectors 2 i -3 j +2 k and 3 i - j -2 k in the ratio 2: 3 , then, we have r = 3(2 i -3 j +2 k )+2(3 i - j -2 k ) 3+2 = 12 i -11 j +2 k 5 r = 1 5 (12 i -11 j +2 k )= 12 5 i - 11 5 j + 2 5 k Now, distance of C from the point with position vector 2 i - j + k is aligned & D= | ( 12 5 -2 ) i + ( -11 5 +1 ) j + ( 2 5 -1 ) k | & = | 2 5 i - 16 5 j - 3 5 k | & D= 4 25 + 36 25 + 9 25 & D= 7 5 aligned