Question

If the position vector of the mid-point of the line segment EF is 4i+ 7j and the position vector of the point E is -3i-4j , find the position vector of the point F.​

Answer 1

Let the position vector of point F be denoted by vector "r". Since the midpoint of the line segment EF is given by (4i+7j), we can use the midpoint formula to find the position vector of point F as follows:

Midpoint of EF = (Position vector of E + Position vector of F)/2

(4i+7j) = (-3i-4j + r)/2

Multiplying both sides by 2, we get:

8i + 14j = -3i - 4j + r

Simplifying the equation, we can isolate the vector "r" on one side:

r = 8i + 14j + 3i + 4j

r = 11i + 18j

Therefore, the position vector of point F is 11i + 18j.