Question
Download Solution PDFसदिश \(\vec a = \hat i + \hat j - \hat k \ and \ \vec b =\hat i - \hat j - \hat k\) के बीच का कोण ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि \(\rm \vec{a} \ and \ \vec b\) दो सदिश हैं, तो \(\rm \vec{a}.\vec{b}=|\vec{a}||\vec{b}|cosθ\) है।
सूचना: यदि सदिश \(\rm \vec{a} \ and \ \vec b\) एक-दूसरे के लंबवत है, तो \(\rm \vec{a}.\vec{b}=0\) है।
गणना:
दिया गया है:
\(\vec a = \hat i + \hat j - \hat k \ and \ \vec b =\hat i - \hat j - \hat k\)
माना कि θ सदिश \(\rm \vec{a} \ and \ \vec b\) के बीच का कोण है।
⇒ \(|\vec a| = \sqrt 3 \ and \ |\vec b| = \sqrt 3\)
हम जानते हैं कि,
\(\rm \vec{a}.\vec{b}=|\vec{a}||\vec{b}|cosθ\)
⇒ \((\hat i + \hat j - \hat k) \cdot (\hat i - \hat j - \hat k) = \sqrt 3 \times \sqrt 3 \times cos θ \)
⇒ 1 = 3 cos θ
⇒ \(\rm cos\ θ=\frac{1}{3}\)
⇒ \(\rm θ=cos^{-1}\frac{1}{3}\)
अतः विकल्प 3 सही है।
Last updated on Jun 20, 2025
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