p का मान ज्ञात कीजिए जिसके लिए  \(p(\hat{i}+\hat{j}+\hat{k})\) एक इकाई सदिश है?

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  1. \(\pm\frac{1}{{\sqrt 3 }}\)
  2. \(\pm\frac{2}{{\sqrt 3 }}\)
  3. \(\pm\frac{1}{{ 3 }}\)
  4. \({{\sqrt 3 }}\)

Answer (Detailed Solution Below)

Option 1 : \(\pm\frac{1}{{\sqrt 3 }}\)
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दिया गया:

\(p(\hat{i}+\hat{j}+\hat{k})\) एक इकाई सदिश है।

संकल्पना:

एक सदिश का एक इकाई सदिश मूल सदिश की तरह इकाई परिमाण और दिशा का एक सदिश होता है।

सूत्र:

सदिश aî + bĵ + ck̂ का परिमाण √(a2 + b2 +c2) द्वारा दिया जाता है।

गणना:

दिए गए सदिश  \(p(\hat{i}+\hat{j}+\hat{k})\) के परिमाण की गणना इस प्रकार की जा सकती है;

\(p(\hat{i}+\hat{j}+\hat{k})\)|= |p|√(12 + 12 + 12)

= |p|√3

यह एक इकाई सदिश है:

⇒ |p|√3 = 1

⇒ |p| = 1/√3

या p = ±1/√3

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