COMEDK 2022

If 2 and 3 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is

The line \(\frac{x-3}{4}=\frac{y-4}{5}=\frac{z-5}{6}\) is parallel to the plane

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

The point of intersection of the lines \({{x - 1} \over 1} = {{y - 1} \over 2} = {{z - 2} \over 3}\) and \({{x -5} \over 2} = {{y - 2} \over 1} = z\) is

Find the general solution of \(\sin 2x + \cos x = 0\).

If \(\sin A+\sin B=a\) and \(\cos A+\cos B=b\), then \(\cos (A+B)\) equals?

What is \({{\cos \theta } \over {1 - \tan \theta }} + {{\sin \theta } \over {1 - \cot \theta }}\) equal to?

If \(\theta\) be the angle between the vectors \(a = 2\widehat i + 2\widehat j - \widehat k\) and \(b = 6\widehat i - 3\widehat j + 2\widehat k\), then

If x, y and z are non-zero real numbers and \(a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k\) and \(c = x\widehat i + y\widehat j + z\widehat k\) are such that \(a \times b = z\widehat i - 3\widehat j + \widehat k\), then [a b...

If \(\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}\) and \(\mathbf{r}=\hat{i}+\hat{k}\), then the unit vector in the direction of \(3 p+q-2 r\) is