Question
Download Solution PDFदिया गया है कि a̅ = 3i̅ - 8j̅ + k̅ और b̅ = 4i̅ + 3j̅ - λk̅ है। यदि a̅ + b̅ = 7i̅ - 5j̅ - 3k̅, तो λ का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
a̅ = 3i̅ - 8j̅ + k̅ और b̅ = 4i̅ + 3j̅ - λk̅।
यदि a̅ + b̅ = 7i̅ - 5j̅ - 3k̅,
अवधारणा:
सदिशों के योग की अवधारणा का प्रयोग कीजिए।
साथ ही दो सदिश बराबर होते हैं, जब i, j और k के गुणांक बराबर होता है।
गणना:
a̅ = 3i̅ - 8j̅ + k̅ और b̅ = 4i̅ + 3j̅ - λk̅
\(\rm \vec{a}+\vec{b}=(3i̅ - 8j̅ + k̅)+( 4i̅ + 3j̅ - λk̅) \)
\(\rm 7i̅ - 5j̅ - 3k̅=(7i̅ - 5j̅ + (1-\lambda)k̅)\)
दोनों पक्षों के गुणांक की तुलना करने पर,
हमें प्राप्त होता है,
- 3 = 1 - λ
⇒ λ = 4
अतः विकल्प (4) सही है।
Last updated on Jun 18, 2025
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