Vector Projection and Quadratic Roots (Jee Mains)

Scalar and Vector Products

Medium

Vector Projection and Quadratic Roots

Let $\overrightarrow {AB} = 2\widehat i + 4\widehat j-5\widehat k$ and $\overrightarrow {AD} = \widehat i + 2\widehat j + \lambda \widehat k,\lambda \in {\Bbb R}$ . Let the projection of the vector $\overrightarrow v = \widehat i + \hat j + \hat k$ on the diagonal $\overrightarrow {AC}$ 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

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