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INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSINTRODUCTION TO THREE DIMENSIONAL GEOMETRY2 Marks
Question
Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio 2 : 3 internally.
✓

Answer

Let P(x, y, z) be any point which divides the line segment joining points A(-2, 3, 5) and B(1, -4, 6) in the ratio 2 : 3 internally.
Then x = $ \frac{{2 \times 1 + 3 \times - 2}}{{2 + 3}} = \frac{{2 - 6}}{5} = \frac{{ - 4}}{5}$
y = $\frac{{2 \times - 4 + 3 \times 3}}{{2 + 3}} = \frac{{ - 8 + 9}}{5} = \frac{1}{5}$
z = $\frac{{2 \times 6 + 3 \times 5}}{{2 + 3}} = \frac{{12 + 15}}{5} = \frac{{27}}{5}$
$\therefore$ Coordinates of P are$\left( {\frac{{ - 4}}{5},\frac{1}{5},\frac{{27}}{5}} \right)$.

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