Let the volume of a parallelepiped whose coterminous edges are given by $ \vec{u}=\hat{i}+\hat{j}+\lambda \hat{k}, \vec{v}=\hat{i}+\hat{j}+3 \hat{k} $ and $ \vec{w}=2 \hat{i}+\hat{j}+\hat{k} $ be $ 1 $ cu. unit. If $ \theta $ be the angle between the edges $ \vec{u} $ and $ \vec{w} $, then the value of $ \cos \theta $ can be

Question

Let the volume of a parallelepiped whose coterminous edges are given by $ \vec{u}=\hat{i}+\hat{j}+\lambda \hat{k}, \vec{v}=\hat{i}+\hat{j}+3 \hat{k} $ and $ \vec{w}=2 \hat{i}+\hat{j}+\hat{k} $ be $ 1 $ cu. unit. If $ \theta $ be the angle between the edges $ \vec{u} $ and $ \vec{w} $, then the value of $ \cos \theta $ can be, $ \frac{1}{33} $, $ \frac{7}{6 \sqrt{3}} $, $ \frac{3}{2} $, $ \frac{5}{3 \sqrt{3}} $

MARKS App · Accepted Answer

± 1 = 1 1 λ 1 1 3 2 1 1 ⇒ = - λ + 3 = ± 1 ⇒ λ = 2 o r λ = 4 For λ = 4 c o s θ = 2 + 1 + 4 6 18 = 7 6 3

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