For what value of - - the vectors - a-2-3-k- and - b-2k- are perpendicular to each other-

Given: a⃗ = 3 î 3 λĵ + k̂ b⃗ = î + ĵ 2 k̂ ∵a⃗⊥b⃗ ∴a⃗·b⃗ = 0 ( #160;3 î 3 λĵ + k̂) ·( î + ĵ 2 k̂) = 0 ⇒ 3 3 λ 2 = 0 ...

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Standard XII

Mathematics

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For what valu...

Question

For what value of $λ$ , the vectors $\to a = 2^i - 3 λ^j +^k$ and $\to b =^i +^j - 2^k$ are perpendicular to each other?

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Solution

Given:-
$\to a = 3^i - 3 λ^j +^k$
$\to b =^i +^j - 2^k$
$∵ \to a ⊥ \to b$
$∴ \to a \cdot \to b = 0$
$(3^i - 3 λ^j +^k) \cdot (^i +^j - 2^k) = 0$
$\Rightarrow 3 - 3 λ - 2 = 0$
$\Rightarrow 3 λ = 1$
$\Rightarrow λ = \frac{1}{3}$

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For what value of $λ$ , the vectors $\to a = 2^i - 3 λ^j +^k$ and $\to b =^i +^j - 2^k$ are perpendicular to each other?

Given:-
$\to a = 3^i - 3 λ^j +^k$
$\to b =^i +^j - 2^k$
$∵ \to a ⊥ \to b$
$∴ \to a \cdot \to b = 0$
$(3^i - 3 λ^j +^k) \cdot (^i +^j - 2^k) = 0$
$\Rightarrow 3 - 3 λ - 2 = 0$
$\Rightarrow 3 λ = 1$
$\Rightarrow λ = \frac{1}{3}$

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For what value of λ, the vectors →a=2^i−3λ^j+^k and →b=^i+^j−2^k are perpendicular to each other?

Given:-→a=3^i−3λ^j+^k→b=^i+^j−2^k∵→a⊥→b∴→a⋅→b=0(3^i−3λ^j+^k)⋅(^i+^j−2^k)=0⇒3−3λ−2=0⇒3λ=1⇒λ=13

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For what value of $λ$ , the vectors $\to a = 2^i - 3 λ^j +^k$ and $\to b =^i +^j - 2^k$ are perpendicular to each other?

Given:-
$\to a = 3^i - 3 λ^j +^k$
$\to b =^i +^j - 2^k$
$∵ \to a ⊥ \to b$
$∴ \to a \cdot \to b = 0$
$(3^i - 3 λ^j +^k) \cdot (^i +^j - 2^k) = 0$
$\Rightarrow 3 - 3 λ - 2 = 0$
$\Rightarrow 3 λ = 1$
$\Rightarrow λ = \frac{1}{3}$