Question

The point A has a position vector 11i−4j and the point B has a position vector 21i+j. Determine the position vector of the point C, which lies between A and B, such that AC:CB is 2:3.

a. 13i−5j
b. 16i−3j
c. 15i−2j
d. 14i−4j

Answer 1

To find the position vector of point C, interpolate between the position vectors of point A and point B using the given ratio. By finding the difference in x and y components, multiplying them by the ratio, and adding them to the components of point A, we can determine the position vector of point C as 15i - 2j. Hence, option c. is correct.

Step-by-step explanation:

To find the position vector of point C, we need to calculate how much of AB is in the ratio 2:3. We can do this by using the concept of linear interpolation. Let's calculate the position vector of point C:

1. Find the difference between the x-components and y-components of the position vectors of points A and B: Δx = 21 - 11 = 10 and Δy = 1 - (-4) = 5.
2. Multiply Δx and Δy by 2/5 (since the ratio AC:CB is 2:3) to get the difference of x and y components of the position vector of point C: Δx_C = 2/5 * 10 = 4 and Δy_C = 2/5 * 5 = 2.
3. Add the components of point A to Δx_C and Δy_C to get the position vector of point C: C = (11 + 4)i + (-4 + 2)j = 15i - 2j.

Therefore, the position vector of point C is 15i - 2j.