The point which divides the line joining the points (1, 3, 4)and (4, 3, 1) internally in the ratio 2: 1, is

Question

The point which divides the line joining the points (1, 3, 4)and (4, 3, 1) internally in the ratio 2: 1, is (A) (2, -3, 3) (B) (2, 3, 3) (C) ((5/2), 3, (5/2)) (D) (-3, 3, 2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7a6e71abbe90e3d3c96b2e130f0f1648-.png" /> ∴ R(x, y, z)=((2 × 4+1 × 1/2+1), (2 × 3+1 × 3/2+1),. .(2 × 1+1 × 4/2+1)) =((9/3), (9/3), (6/3))=(3,3,2)

Q. The point which divides the line joining the points (1, 3, 4)and (4, 3, 1) internally in the ratio $2 : 1$ , is

(2, -3, 3)

(2, 3, 3)

$(\frac{5}{2}, 3, \frac{5}{2})$

$(- 3, 3, 2)$

(3, 3, 2)

$∴ R (x, y, z) = (\frac{2 \times 4 + 1 \times 1}{2 + 1}, \frac{2 \times 3 + 1 \times 3}{2 + 1}, \frac{2 \times 1 + 1 \times 4}{2 + 1})$
$= (\frac{9}{3}, \frac{9}{3}, \frac{6}{3}) = (3, 3, 2)$

Q. The point which divides the line joining the points (1, 3, 4)and (4, 3, 1) internally in the ratio 2:1, is