COMEDK 2021

The line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) is parallel to the plane

The equation of a plane passing through the line of intersection of the planes \(x+2y+3z=2,x-y+z=3\) and at a distance \(\frac{2}{\sqrt3}\) from the point \((3,1,-1)\) is

The angle between the lines \(2x=3y=-z\) and \(6x=-y=-4z\) is

The point of intersection of the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 4} \over 5} = {{y - 1} \over 2} = z\) is

If \(\sin 2x = 4\cos x\), then x is equal to

If x and y are acute angles, such that \(\cos x + \cos y = {3 \over 2}\) and \(\sin x + \sin y = {3 \over 4}\), then \(\sin (x + y)\) equals

The expression \({{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}\) can be written as

The vector that must be added to \(\widehat i - 3\widehat j + 2\widehat k\) and \(3\widehat i + 6\widehat j - 7\widehat k\) so resultant vector is a unit vector along the X-axis is

If |a| = 8, |b| = 3 and |a \(\times\) b| = 12, then find the angle between a and b.

If for \(a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k\) and \(c = - 3\widehat i + \widehat j + 2\widehat k\), then find \([a\,b\,c]\).