Three Dimension...

The projection of a directed line segment on the co-ordinate axes are $$12,4,3$$, then the direction cosines of the line are

A line OP where O $$=$$ $$(0, 0, 0)$$ makes equal angles with ox, oy, oz. The point on OP, which is at a distance of $$6$$ units from O is:

The direction ratios of a normal to the plane through $$(1, 0, 0)$$ and $$(0, 1, 0)$$, which makes an angle of $$\dfrac {\pi}{4}$$ with the plane $$x+y=3$$, are:

What is the equation of the plane which passes through the z-axis and its perpendicular to the line $$\dfrac {x-a}{cos\theta}=\dfrac {y+2}{sin\theta}=\dfrac {z-3}{0} ?$$

If a line makes an angle of $$\dfrac {\pi}{4}$$ with the positive direction of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of $$z$$-axis is-

The equation of the plane passing through the lines $$\frac {x-4}{1}=\frac {y-3}{1}=\frac {z-2}{2}$$ and $$\frac {x-3}{1}=\frac {y-2}{-4}=\frac {z}{5}$$ is-

A line makes an angle $$\theta$$ with each of the $$x$$- and $$z$$- axes. If the angle $$\beta$$, which it makes with the $$y$$-axis, is such that $$\sin^2\beta=3 \sin^2\theta$$, then $$\cos^2\theta$$ equals-

For waht value of $$\lambda$$ , the three numbers $$2\lambda  - 1 , \frac{1}{4}, \lambda -\frac{1}{2}$$ can be the direction cosines of a straight line?

If the foot of the perpendicular from the origin to a plane is $$P(a, b, c)$$, the equation of the plane is-

If the points $$(-1, 3, 2), (-4, 2, -2)$$ and $$(5, 5, \lambda)$$ are collinear, then $$\lambda$$ is equal to