If the vectors 4-7-2k- -5-3k- 3-k- form a triangle- then the value of - is equal to

Using triangle law of vectors, a = b + nbsp; c ⇒ 4î 7ĵ 2k̂ = î+5ĵ 3k̂ + 3î λĵ+k̂ ⇒4î 7ĵ 2k̂ = 4î +(5 λ)ĵ + ( 3+1)k̂ On comparing, we get 5 λ nbsp; = 7 ⇒λ ...

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Standard XII

Mathematics

Skew Lines

If the vector...

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

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Solution

Using triangle law of vectors,
$\to a = \to b + \to c$
$\Rightarrow 4^i - 7^j - 2^k =^i + 5^j - 3^k + 3^i - λ^j +^k$
$\Rightarrow 4^i - 7^j - 2^k = 4^i + (5 - λ)^j + (- 3 + 1)^k$
On comparing, we get
$5 - λ = - 7$
$\Rightarrow λ = 12$

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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

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

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

Using triangle law of vectors,
$\to a = \to b + \to c$
$\Rightarrow 4^i - 7^j - 2^k =^i + 5^j - 3^k + 3^i - λ^j +^k$
$\Rightarrow 4^i - 7^j - 2^k = 4^i + (5 - λ)^j + (- 3 + 1)^k$
On comparing, we get
$5 - λ = - 7$
$\Rightarrow λ = 12$