KCET 2022

The coordinates of foot of the perpendicular drawn from the origin to the plane \(2 x-3 y+4 z=29\) are

The angle between the pair of lines \(\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}\) and \(\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}\) is

The distance of the point whose position vector is \((2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})\) from the plane \(\mathbf{r} \cdot(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=4\) is

The trigonometric function \(y=\tan x\) in the II quadrant

The degree measure of \(\frac{\pi}{32}\) is equal to

The value of \(\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}\) is

\(\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}}=\)

If \(|\mathbf{a}|=2\) and \(|\mathbf{b}|=3\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then the length of the vector \(\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|\) is

If \(|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36\) and \(|\mathbf{a}|=3\), then \(|\mathbf{a}|\) is equal to

If \(\alpha=\hat{\mathbf{i}}-3 \hat{\mathbf{j}}, \beta=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\), then express \(\beta\) in the form \(\beta=\beta_1+\beta_2\) where \(\beta_1\) is parallel to \(\alpha\) and \(\beta_2\) is perpe...