Three Dimension...

If direction cosines of a vector of magnitude $$3$$ are $$\dfrac {2}{3}, -\dfrac {1}{3}, \dfrac {2}{3}$$ and $$a > 0$$, then vector is ____

If a plane passing through the point $$(2, 2, 1)$$ and is perpendicular to the planes $$3x + 2y + 4z + 1 = 0$$ and $$2x + y + 3z + 2 = 0$$. Then, the equation of the plane is

If a line segment $$OP$$ makes angles of $$\dfrac {\pi}{4}$$ and $$\dfrac {\pi}{3}$$ with X-axis and Y-axis, respectively. Then, the direction cosines are

If a line makes $${ 45 }^{ o }$$, $${ 60 }^{ o }$$ with positive direction of axes $$x$$ and $$y$$ then the angles it makes with the $$z$$-axis is

The vector equation of a plane passing through a point whose. P.V. is $$\overrightarrow a$$ and perpendicular to a vector $$\overrightarrow n$$, is

What are the direction cosines of a line which is equally inclined to the positive directions of the axes?

What are the direction ratios of normal to the plane $$2x - y + 2z + 1 = 0$$ ?

What is the sum of the squares of direction cosines of $$x$$-axis?

Let a vector $$\vec{r}$$ make angles $$60^o, 30^o$$ with it and y-axes respectively.Find the angle $$\vec{r}$$ make with z-axis.

What are the direction cosines of $$\vec{r}$$ ?