Question
Download Solution PDFयदि मूल और बिंदु P (2, 3, 4), Q (1, 2, 3) और R (x, y, z) समतलीय हैं तो:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि तीन सदिश समतलीय हैं तो उनका अदिश त्रिक गुणनफल शून्य है।
⇒ \(\rm \vec a.(\vec b\times \vec c) = 0\)
गणना:
दिया है कि मूल और बिंदु P (2, 3, 4), Q (1, 2, 3) और R (x, y, z) समतलीय हैं
⇒ \(\rm \vec a = \vec {OR} = {(x, y, z)}\)
⇒ \(\rm \vec b = \vec {OP} = {(2, 3, 4)}\)
⇒ \(\rm \vec c = \vec {OQ} = {(1, 2, 3)}\)
यहाँ, \(\rm\vec a\) , \(\rm\vec b\) और \(\vec c\) समतलीय हैं
तीन सदिश समतलीय हैं तो यदि उनका अदिश त्रिक गुणनफल शून्य है।
⇒ \(\rm \vec a.(\vec b\times \vec c) = 0\)
⇒ \(\begin{vmatrix} \rm x & \rm y & \rm z\\ 2&3 &4 \\ 1&2 &3 \end{vmatrix} = 0\)
⇒ x(9 - 8) - y(6 - 4) + z (4 - 3) = 0
⇒ x - 2y + z = 0
इसलिए, यदि मूल और बिंदु P (2, 3, 4), Q (1, 2, 3) और R (x, y, z) समतलीय हैं तो x - 2y + z = 0
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