Question
Download Solution PDFयदि a̅ = 3i̅ - 2j̅ + k̅ और b̅ = 4i̅ +3j̅ - λk̅ लांबिक हैं, तो λ = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(\overrightarrow{a}=3\hat i-2\hat j+\hat k \text{ and }\overrightarrow{B}=4\hat i+3\hat j-\lambda \hat k\) .
अवधारणा:
दो सदिशों \(\overrightarrow {a} \text{ and } \overrightarrow{b}\) को लांबिक तब माना जाता है, जब उनके बीच का कोण 90º होता है अर्थात सदिश परस्पर लंबवत होते हैं।
इसलिए, दोनों सदिश \(\overrightarrow {a} \text{ and } \overrightarrow{b}\) का अदिश गुणनफल शून्य होता है।
- \(\overrightarrow{a}.\overrightarrow{b}=|a||b|cos\theta=|a||b|cos90=0\)
गणना:
\(\overrightarrow{a}.\overrightarrow{b}=0\)
\((3\hat i-2\hat j+\hat k).(4\hat i+3\hat j-\lambda \hat k)=0\)
\(12-6-\lambda=0\)
\(\implies\lambda=6\)
सही उत्तर विकल्प A अर्थात 6 है।
Last updated on May 26, 2025
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