Sum of squares of direction cosines =1: cos290+cos260+cos2θ=1. So 0+41+cos2θ=1, giving cos2θ=43. Since θ is acute: cosθ=23, so θ=6π.
If a line makes angles 90 degree, 60 degree and θ with x,y and z axis respectively, where θ is acute, then value of θ is:
Held on 25 May 2023 · Verified 13 Jul 2026.
6π
4π
3π
2π
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The shortest distance between the following lines: $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$ $\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:
The angle between the line $2x = 3y = z$ and $x$- axis is:
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$\sin^{-1}(\cos\frac{3\pi}{5})$ equals
If lines $\frac{x+5}{5\lambda+2} = \frac{4-2y}{10} = \frac{1-3z}{-3}$ and $\frac{x-2}{1} = \frac{1+2y}{4\lambda} = \frac{2+z}{3}$ are perpendicular, than value of '$\lambda$' is
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