Question

Relative to an origin O, the position vectors of points A and B are 3i + 4j − k and 5i − 2j − 3k
respectively.
The point C is the mid-point of AB. The point D is such that OD = 2OB
Find DC

Answer 1

@Compassionate

Answer 2

any ideas ?

Answer 3

AB> is vector B minus vector A

Answer 4

AB = OB - OA ...

Answer 5

yes. AB> is like a line, do you know how to find mid-point of a line given 2 points?

Answer 6

Find the points C and D. For the point C, as it is the point,
\[OC=C=\frac{A+B}{2}=((3,4,-1)+(5,-2,-3))/2=(4,1,-2)\]
Now you have C. Now you have to find D, or better the position vector OD, but you only have to do,
\[OD=2OB=2(5,-2,-3)=(10,-4,-6)\]
Now you have D and C, so,
\[DC=OC-OD=(4,1,-2)-(10,-4,-6)\]

Answer 7

oh ! well I made mistake when working out the mid pt...
Instead of 0.5 ( OA + OB ) I wrote 0.5 ( OB - OA )...