Short Quiz

The equation of a line parallel to the vector \(3 \hat{i}+\hat{j}+2 \hat{k}\) and passing through the point \((4,-3,7)\) is :

If \(l_{1}, \mathrm{~m}_{1}, \mathrm{n}_{1}\) and \(l_{2}, \mathrm{~m}_{2}, \mathrm{n}_{2}\) are direction cosines of lines \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) respectively and \(\theta\) is the acute angle between them, then :

If a line makes an angle of \(\frac{\pi}{4}\) with the positive directions of both \(x\)-axis and \(z\)-axis, then the angle which it makes with the positive direction of \(y\)-axis is :

If a line makes angles of \(\frac{3 \pi}{4}, \frac{\pi}{3}\) and \(\theta\) with the positive directions of \(x, y\) and z -axis respectively, then \(\theta\) is