for a unit cube unit vector along the diagonal
O P = 1 3 ( i ^ + j ^ + k ^ ) < i m g s r c = " / a p i / p r o x y − i m a g e ? u r l = h t t p s \mathrm{OP}=\frac{1}{\sqrt{3}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fbitsat%252F7NTWetRK4yxOBniSvpXeh_Q4dVkdpauFDXCZLGDxbqY.original.fullsize.png%3Falt%3Dmedia \text{ and } clean=1 \text{ and } v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2F7NTWetRK4yxOBniSvpXeh_Q4dVkdpauFDXCZLGDxbqY.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fbitsat%2F7NTWetRK4yxOBniSvpXeh_Q4dVkdpauFDXCZLGDxbqY.original.fullsize.png?alt=media"> OP = 3 1 ( i ^ + j ^ + k ^ ) < im g src = "/ a p i / p ro x y − ima g e ? u r l = h ttp s \\ unit vector along the diagonal
C D = 1 3 ( i ^ + j ^ − k ^ ) ∴ cos θ = 1 3 ( 1 + 1 − 1 ) = 1 3 ∴ tan θ = 2 2 \mathrm{CD}=\frac{1}{\sqrt{3}}(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})\therefore \cos \theta=\frac{1}{3}(1+1-1)=\frac{1}{3} \quad \therefore \tan \theta=2 \sqrt{2} CD = 3 1 ( i ^ + j ^ − k ^ ) ∴ cos θ = 3 1 ( 1 + 1 − 1 ) = 3 1 ∴ tan θ = 2 2 
