If the vectors a = i ^ − j ^ + 2 k ^ , b = 2 i ^ + 4 j ^ + k ^ and c = λ i ^ + j ^ + μ k ^ are mutually orthogonal, then ( λ , μ ) =

a ⋅ b = 0 , b ⋅ c = 0 , c ⋅ a = 0 ⇒ 2 λ + 4 + μ = 0 λ − 1 + 2 μ = 0 Solving we get: λ = − 3 , μ = 2

Home

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorDot Product & Its Application ( Projection etc.)Hard2 minPYQ_2010

MathematicsHardsingle choice

If the vectors $a = \hat{i} - \hat{j} + 2 \hat{k}, b = 2 \hat{i} + 4 \hat{j} + \hat{k}$ and $c = λ \hat{i} + \hat{j} + μ \hat{k}$ are mutually orthogonal, then $(λ, μ) =$

Options:

Answer:

Solution:

$a \cdot b = 0, b \cdot c = 0, c \cdot a = 0 \Rightarrow 2 λ + 4 + μ = 0 λ - 1 + 2 μ = 0$ Solving we get: $λ = - 3, μ = 2$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Dot Product & Its Application ( Projection etc.)

⏱ 2mℹ️ Source: PYQ_2010

Doubts & Discussion

Loading discussions...