If a-2-k-b-2k- and c-3-2-3-k- where - is a constant and a is perpendicular to c-b- then sum of the different values of - is

Given : a=2î ĵ+k̂,b=î+ĵ 2k̂ and c=î+3ĵ (λ^2+3λ)k̂ As, a is perpendicular to c λb, then a·(c λb) = 0 ⇒ nbsp;a·c λa·b= 0 ⇒ 2 3 (λ^2+3λ) λ (2 1 2)=0 ⇒λ^2+2λ+1=0 ...

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Byju's Answer

Standard XI

Mathematics

Applications of Dot Product

If a=2î-ĵ+k̂,...

Question

If $\to a = 2^i -^j +^k, \to b =^i +^j - 2^k$ and $\to c =^i + 3^j - (λ^{2} + 3 λ)^k$ , where $λ$ is a constant and $\to a$ is perpendicular to $\to c - λ \to b$ , then sum of the different values of $λ$ is

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Solution

The correct option is A $- 1$
Given : $\to a = 2^i -^j +^k, \to b =^i +^j - 2^k$ and $\to c =^i + 3^j - (λ^{2} + 3 λ)^k$

As, $\to a$ is perpendicular to $\to c - λ \to b,$ then
$\to a \cdot (\to c - λ \to b) = 0 \Rightarrow \to a \cdot \to c - λ \to a \cdot \to b = 0 \Rightarrow 2 - 3 - (λ^{2} + 3 λ) - λ (2 - 1 - 2) = 0 \Rightarrow λ^{2} + 2 λ + 1 = 0 \Rightarrow (λ + 1)^{2} = 0 ∴ λ = - 1$

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Similar questions

Q. If

\to a = 2^i -^j +^k, \to b =^i +^j - 2^k

and

\to c =^i + 3^j - (λ^{2} + 3 λ)^k

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\to c - λ \to b

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Q. If

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and

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c = 4^i - 3^j - 2^k

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If →a=2^i−^j+^k,→b=^i+^j−2^k and →c=^i+3^j−(λ2+3λ)^k, where λ is a constant and →a is perpendicular to →c−λ→b, then sum of the different values of λ is

The correct option is A −1Given : →a=2^i−^j+^k,→b=^i+^j−2^k and →c=^i+3^j−(λ2+3λ)^k As, →a is perpendicular to →c−λ→b, then →a⋅(→c−λ→b)=0⇒→a⋅→c−λ→a⋅→b=0⇒2−3−(λ2+3λ)−λ(2−1−2)=0⇒λ2+2λ+1=0⇒(λ+1)2=0∴λ=−1

If $\to a = 2^i -^j +^k, \to b =^i +^j - 2^k$ and $\to c =^i + 3^j - (λ^{2} + 3 λ)^k$ , where $λ$ is a constant and $\to a$ is perpendicular to $\to c - λ \to b$ , then sum of the different values of $λ$ is