Question
Download Solution PDFयदि \(\rm \vec{i} - a\vec{j} + 5\vec{k}\) और \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) समानांतर सदिश हैं, तो b किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि \({\rm{\vec a\;and\;\vec b}}\) एक-दूसरे के समानांतर दो सदिश हैं, तो \({\rm\vec{a} = λ \vec{b}}\) या \(\rm \vec{a} × \vec{b} =0\) है।
गणना:
दिया गया है:
\(\rm \vec{i} - a\vec{j} + 5\vec{k}\) और \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) समानांतर सदिश हैं,
इसलिए, \(\rm \vec{i} - a\vec{j} + 5\vec{k}= λ (\rm 3\vec{i} - 6\vec{j} + b\vec{k})\)
\(\rm \vec{i},\vec{j} \;and\; \vec{k}\)के गुणांक को बराबर करने पर
⇒ 1 = 3λ, ∴ λ = 1/3
⇒ -a = -6λ
⇒ 5 = bλ .... (1)
समीकरण (1) में λ का मान रखने पर, हमें निम्न प्राप्त होता है
5 = b × (1/3)
अतः b = 15
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