यदि a̅ = 3i̅ - 2j̅ + k̅ और b̅ = 4i̅ +3j̅ - λk̅ लांबिक हैं, तो λ = ?

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  1. 6
  2. 12
  3. -6
  4. -12

Answer (Detailed Solution Below)

Option 1 : 6
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दिया 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।

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