Question
Download Solution PDFयदि \(\rm \vec a\) एक इकाई सदिश है और \(\rm \left(\vec x + 2\vec a\right) \cdot \left(\vec x - 2\vec a\right) = 12\) है तो \(|\rm \vec x |\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
\(\rm \left(\vec a + \vec b\right) \cdot \left(\vec a - \vec b\right) = \left|\vec a\right|^2-\left|\vec b\right|^2\)
यदि \(\rm \vec u\) एक इकाई सदिश है तो \(\rm \left|\vec u\right|=1\) है।
गणना:
यह दिया गया है कि
\((\rm \vec x + \rm 2\vec a) \cdot (\rm \vec x - \rm 2\vec a) = 12\).
⇒ \(\rm \left|\vec x\right|^2 - 4\left|\vec a\right|^2 = 12\)
चूँकि \(\rm \vec a\) एक इकाई सदिश है, इसलिए हमें निम्न प्राप्त होता है
⇒ \(\rm \left|\vec x\right|^2 - 4= 12\)
⇒ \(\rm \left|\vec x\right|^2 =16\)
⇒ \(|\rm \vec x |\) = 4
Last updated on May 30, 2025
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