The point C(0, 1, 2) lies on the line segment joining the points A(2, −3, 4) and B(−3, 7, −1). The point C divides AB in the ratio
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 : 3 internally
Let C divide AB in the ratio k : 1. By the section formula, the x-coordinate of C is
\( \displaystyle \frac{k(-3)+1(2)}{k+1} = 0 \)
\(-3k+2 = 0\)
\( \displaystyle k = \frac{2}{3} \)
k is positive, so the division is internal, in the ratio 2 : 3. The other coordinates agree:
\( \displaystyle y = \frac{2(7)+3(-3)}{5} = \frac{5}{5} = 1 \)
\( \displaystyle z = \frac{2(-1)+3(4)}{5} = \frac{10}{5} = 2 \)