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Question
If the vectors 4^i−7^j−2^k, ^i+5^j−3^k, 3^i−λ^j+^k, form a triangle, then the value of λ is equal to
If the vectors 4^i−7^j−2^k, ^i+5^j−3^k, 3^i−λ^j+^k, form a triangle, then the value of λ is equal to
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Solution
Using triangle law of vectors,
→a=→b+→c
⇒4^i−7^j−2^k=^i+5^j−3^k+3^i−λ^j+^k
⇒4^i−7^j−2^k=4^i+(5−λ)^j+(−3+1)^k
On comparing, we get
5−λ=−7
⇒λ=12
→a=→b+→c
⇒4^i−7^j−2^k=^i+5^j−3^k+3^i−λ^j+^k
⇒4^i−7^j−2^k=4^i+(5−λ)^j+(−3+1)^k
On comparing, we get
5−λ=−7
⇒λ=12
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