Let \overrightarrow{ AB }=2 \hat{i}+4 \hat{j}-5 \hat{k} and \overrightarrow{ AD }=\hat{i}+2 \hat{j}+\lambda \hat{k}, \lambda \in R. Let the projection of the vector \overrightarrow{v}=\hat{i}+\hat{j}+\hat{k} on the diagonal \overrightarrow{ AC } of the parallelogram ABCD be of length one unit. If \alpha, \beta, where \alpha>\beta, be the roots of the equation \lambda^2 x^2-6 \lambda x+5=0, then 2 \alpha-\beta is equal to [22 Jan 2026 Shift 1]

Vector Algebra Part 3

Section: Mathematics

Question : 14 of 72

Marks: +1, -0

Let

→

∧

−5

∧

and

→

∧

+λ

∧

,λ∈R. Let the projection of the vector

→

∧

on the diagonal

→

of the parallelogram ABCD be of length one unit. If α,β, where α>β, be the roots of the equation λ2x2−6λx+5=0, then 2α−β is equal to

[22 Jan 2026 Shift 1]

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