Let A(-1,2,1) and B(4,3,5) be two given points the projection of AB on a line which makes angle 120∘ and 135∘with Y axis and Z axis respectively and an acute angle with X- axis is λ−λ2 then λ=

cos2α+cos2120∘+cos2135∘=1⇒cosα=12(-ve not possible)⇒α=60∘Projection of AB =124+1−123−2−125−1=2−22∵λ=2

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Let A(-1,2,1) and B(4,3,5) be two given points the projection of AB on a line which makes angle $120^{\circ}$ and $135^{\circ}$ with Y axis and Z axis respectively and an acute angle with X- axis is $(λ - λ \sqrt{2})$ then $λ =$

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$\cos^{2} α + \cos^{2} 120^{\circ} + \cos^{2} 135^{\circ} = 1$

$\Rightarrow \cos α = \frac{1}{2}$ (-ve not possible)

$\Rightarrow α = 60^{\circ}$

Projection of AB $= \frac{1}{2} (4 + 1) - \frac{1}{2} (3 - 2) - \frac{1}{\sqrt{2}} (5 - 1)$

$= 2 - 2 \sqrt{2}$

$∵ λ = 2$

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