Three Dimension...

A plane passes through the point $$(0, -1, 0)$$ and $$(0, 0, 1)$$ and makes an angle of $$\dfrac{\pi}{4}$$ with the plane $$y-z=0$$ then the point which satisfies the desired plane is?

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is?

The angle between two adjacent sides $$\vec { a } $$ and $$\vec { b } $$ of parallelogram is $$\cfrac{\pi}{6}$$. If $$\vec { a } =\left( 2,-2,1 \right) $$ and $$\left| \vec { b }  \right| =2\left| \vec { a }  \right| $$, then area of this parallelogram is ______

The equation of the plane passing through the point $$(-1, 2, 1)$$ and perpendicular to the line joining the points $$(-3, 1, 2)$$ and $$(2, 3, 4)$$ is ________.

The direction ratios of the line perpendicular to the lines

The projections of a line segment on $$X, Y$$ and $$Z$$ axes are $$12, 4$$ and $$3$$ respectively. The length and direction cosines of the line segment are

A line passes through the point $$A(-2,4,-5)$$ and is parallel to the line $$\cfrac{x+3}{3}=\cfrac{y-4}{5}=\cfrac{z+8}{6}$$. The vector equation of the line is

A line passes through the point $$A(5,-2,4)$$ and it is parallel to the vector $$\left(2 \hat { i } -\hat { j } +3\hat { k }  \right) $$. The vector equation of the line is

The Cartesian equations of a line are $$\cfrac{x-1}{2}=\cfrac{y+2}{3}=\cfrac{z-5}{-1}$$. Its vector equation is

The angle between the lines $$\cfrac{x}{2}=\cfrac{y}{2}=\cfrac{z}{1}$$ and $$\cfrac{x-5}{4}=\cfrac{y-2}{1}=\cfrac{z-3}{8}$$ is