KCET 2020

The distance of the point \((1,2,-4)\) from the line \(\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}\) is

The point \((1,-3,4)\) lies in the octant

The sine of the angle between the straight line \(\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}\) and the plane \(2 x-2 y+z=5\) is

If a line makes an angle of with each of \(X\) and \(Y\)-axis, then the acute angle made by Z-axis is

The value of \(\sin ^2 51^{\circ}+\sin ^2 39^{\circ}\) is

If \(\tan A+\cot A=2\), then the value of \(\tan ^4 A+\cot ^4 A=\)

If \(|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6\), then \(|\mathbf{b}|\) is equal to

If \(\mathbf{a}\) and \(\mathbf{b}\) are unit vectors and \(\theta\) is the angle between \(\mathbf{a}\) and \(\mathbf{b}\), then \(\sin \frac{\theta}{2}\) is equal to

If the vectors \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are coplanar, then the value of $$\lambda...

The two vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) represent the two sides \(\overline{A B}\) and \(\overline{A C}\) respectively of a \(\triangle A B C\). Th...