If a -2 -k- b -2 k- and c -3 -2-3 - k- where - is a constant and a is perpendicular to c - b- then sum ofthe different values of - isA- -1B- 2C- 1D- -2

The correct option is A 1Given : 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+ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a =2 î-ĵ+k...

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

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If $a = 2^i + 2^j + 3^k$ , $b = -^i + 2^j +^k$ and $c = 3^i +^j$ such that $a + λ b$ is perpendicular to c, then find the value of $λ$ .

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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