Question

The position vectors of points C and D are 2i + 37 and 7i + 5i respectively. Find the position vector of a point H which divides the line PQ in the ratio of 2: 3.​

Answer 1

Explanation:

Let P be the point C with position vector 2i + 3j and Q be the point D with position vector 7i + 5j. We want to find the position vector of point H which divides PQ in the ratio 2:3.

Let the position vector of point H be r. Then we have:

PH/PQ = 2/3

(P - r)/(Q - r) = 2/3

Multiplying both sides by (Q - r), we get:

P - r = (2/3)(Q - r)

Expanding the brackets and rearranging, we get:

r = (2Q + 3P)/5

Substituting the position vectors of P and Q, we get:

r = (2(7i + 5j) + 3(2i + 3j))/5

= (14i + 10j + 6i + 9j)/5

= (20i + 19j)/5

= 4i + 3.8j

Therefore, the position vector of point H is 4i + 3.8j.