INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSINTRODUCTION TO THREE DIMENSIONAL GEOMETRY3 Marks
Question
Show that the points P (–2, 3, 5), Q (1, 2, 3) and R (7, 0, –1) are collinear.
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Answer
We know that points are said to be collinear if they lie on a line Now, $\mathrm{PQ}=\sqrt{(1+2)^{2}+(2-3)^{2}+(3-5)^{2}}=\sqrt{9+1+4}=\sqrt{14}$ $\mathrm{QR}=\sqrt{(7-1)^{2}+(0-2)^{2}+(-1-3)^{2}}=\sqrt{36+4+16}=\sqrt{56}=2 \sqrt{14}$ and $\mathrm{PR}=\sqrt{(7+2)^{2}+(0-3)^{2}+(-1-5)^{2}}=\sqrt{81+9+36}=\sqrt{126}=3 \sqrt{14}$ Thus, PQ + QR = PR Hence, P, Q and R are collinear.
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